First week March 2022 - I'm going to Munich

Since I went back to Mexico, and I started typing here again, I promised to myself I'd do it more often, the reason being that it provides a sort of catharsis, even if I don't always write about matters directly affecting me. Where I go wrong, methinks, is in trying to provide much detail or in trying to satisfy an imaginary audience, which in the end derives in it taking a much longer time and effort than it should.

I'll soon be leaving Taipei and gonna be heading to Munich. I've taken a job with IQM as a quantum physics engineer, where I'll work mainly characterizing their superconducting device and thinking about error mitigation/correction.

By the way, we put up a new paper on the arXiv recently on more RB for non-Markovian noise. Despite this one being less sexy than its predecessor when it comes to plots or figures (spoiler alert, there is none at all), I feel like it is hot nevertheless, mathematically and physically, even though as always, there are things that can be improved or addressed further.

Towards a general framework of Randomized Benchmarking for non-Markovian Noise
Pedro Figueroa-Romero, Kavan Modi, Min-Hsiu Hsieh

I will be cutting my 2-year contract in Taipei to a single year, with the main reason being twofold: the first is that the borders are not yet opening, and the second is the lack of diversity, mainly in the workplace. To be fair, people have been great with me, especially the team leader and director of the institute, Min-Hsiu Hsieh.

When it comes to IQM, from the places I sent requests or applications to, it was, I would say, my second priority: to be honest, Zapata was the first one, although mostly for selfish reasons (essentially I don't think I had quite the right profile for any of their vacancies). Regardless, I am super excited about taking up my role; ironically, without my year in Taipei, I don't think I would've been perceived as having the right profile, or it would've been much more difficult getting in. Also, the topic of device characterization in general has revived much of the passion I'd lost for research.

About Munich, so far the only issue I have is the high costs of living coupled with the high taxing rates. Even though I will be earning more than what I currently am, I will be having quite less after taxes and accommodation, which is a tad depressing. I guess it's a reason why the expats that decide to come to Taiwan like it so much, cause you can afford a much higher quality life with much less.

One thing I'll totally be missing is riding a bike, which was, unexpectedly, an amazing experience! This weekend at last I went around the north coast, only with a little climb at the beginning in Fengguizui. I'd been wanting to do this ride for a while, so I decided it was now or never, and didn't disappoint, even reminded me a bit of Beach Rd in Melbourne. I also took the chance to visit the Temple of Eighteen Lords again!

Fourteentine, Taiwanese bureaucracy and loneliness

I started typing this entry in the middle of the mandatory 14-day quarantine* imposed by Taiwan on anyone entering the country, and never really got to complete it, even when I was trapped in that hotel room 24/7. As everything in life, while in quarantine it felt like it would never end (the day after it finished, my feeling was even a bit surreal and I felt kind of afraid of having to face the outside world), but now it feels like it went by in the blink of an eye. I guess all I can complain about was the absurdly high price of the quarantine hotel, but at least I was treated well and really had all I needed to make it through.

For some reason I sometimes feel that writing in here does not make sense at all, and some others I feel that not only is it good for me mentally but it leaves some more permanent information about my thoughts when I'm gone, or when I might need to recall some things. I'm, at least at this second, trying to commit myself to write at least once a week, without caring much about detail, which is, I think, what deters me in the first place from writing or at least keeps me from concluding whatever thought process I want to capture in writing. I guess I just have to forget a bit about style detail and precision when it comes to this thing.

Anyhow, my first status complain is that bureaucracy in Taiwan is an absolute drag. It's funny because I used to think about Taiwan as some very technologically advanced country which would have automated many things and would be very efficient in dealing with many formalities. This is just not so, and some things even seem to make little sense. To be fair, many things do work to a great extent like the strictness they've had with covid-19 and so on. Anyhow, I concluded my quarantine on May the 4th and got sorted almost all bureaucratic chores I needed to. I'm very much looking forward to resuming my life.

While being a postdoc abroad definitely feels different to being a PhD student abroad because of the professional part, there are things in personal life that do feel like going back in time in a negative way. And this is especially true if one is single (i.e. not married) and faces being in a new place with no acquaintances; add to this the unusual circumstance where you're required to initially isolate yourself at least for 22 days and things get a bit worse. And don't get me wrong, it's great to have a life experience like this and being able to live in different places and truly immerse yourself in a totally different environment, but I guess at some point it feels a bit exhausting, even more if you feel that you actually can't call this or that place home.

Today I was particularly reminded of this because I grabbed my camera and went out to check Taipei 101 (台北101) and Elephant Mountain (象山). This kind of reminded me of some shitty times in Melbourne by my own, even when actually trying some photography sort of helped me feel better back then. It also somehow intensified the uneasiness of being in a long-distance relationship (LDR). As I tried to elaborate some entries below, it's just impossible to remain the same person and there is just no way of genuinely sharing feelings all the time when both eventually live through entirely different things. Now, surely some people can empathise better than others, and I guess the first is the type that eventually make it through in LDRs.

* Quarantine literally implies a 40-day isolation period. In Spanish this is easily adapted to imply a 14-day period turning the word 'cuarentena' into 'catorcena'. Or well, okay, maybe not.

Timing

Someone told me the other day that things tend to happen in their right moment, even if we feel that they are taking too long or that others have taken too short.

While certainly this cannot be objectively true (things can always happen more favourably), it reminded me of two popular sayings:

Los tiempos de Dios son perfectos. (The timings of God are perfect.)

Cuando te toca, ni aunque te quites, y cuando no te toca, ni aunque te pongas. (When it's your time, it doesn't matter if you move away, and when it's not, doesn't matter if you put in place.)

While I rationally wanna hold that thinking in this way is a means of comforting oneself with whatever outcomes we get in life, I like the feeling of letting go of things I cannot control and just admit that there are things I will never be able to comprehend.

Freedom, responsibilities and losing my mind

So far, all major transitions in my academic —or professional if you'd consider a PhD a real job— life have taken quite long, with more or less fault of my own.

When I first entered university, I was already a year behind because I'd dropped out of high-school before and hadn't had my diploma ready (surprisingly for me and all who knew me back then, I passed the standardised test to enter the major Mexican university, UNAM to study Economics).

Then on the undergrad to master's transition I lost a year from when I finished to when I started in Edinburgh; while this was my fault to a degree, it was a choice and the wait was virtually inevitable, I honestly don't remember many highlights of that year other than attending the graduation (which I did mostly to thank my parents), doing a s**tton of bureaucracy and attending some schools and conferences as a non-presenting student. In this stage my life continued almost normally and I had my friends and family; what was painful was the whole wait of outcomes: the English test (IELTS in my case), the university applications (if I remember correctly I narrowed my options to only two programs in the UK, the other was at Uni Glasgow and I turned it down), the scholarship(s) and the visa. I wrote about this back in the day (in Spanish) and the whole timing was just right, I don't think it could've been done much differently. In any case, as I said, it was totally worth it, that was literally the second time I stepped on a plane (first on my own and first travelling abroad) and the whole thing made me mature and grow incommensurately.

Then the master's to PhD transition lasted half a year (Oct 16 to March 17), which wasn't so bad, considering I only started looking and applying shortly after back in Mexico; here the major issue was the uncertainty of not knowing where I'd end up or what I'd end up doing: back in Edinburgh I had focused on theoretical particle physics and I was looking for alternatives, as I wasn't keen on pursuing research in the field, I even remember sending a couple of emails to do research in renewable energies! The only other good offer I remember turning down was a doctorate in Probability and Statistics at CIMAT. The longest wait was for the paperwork in the university, I only had an informal offer from my supervisor but the formal acceptance took some 3 to 4 months; surprisingly the visa process was extremely quick, I just had to fill some forms and take the letter from the university and in a couple of days my visa was ready. I remember some really bad days and this time the feeling that I was already too old to be living at my mother's house and being paid everything started to bother me; I also didn't get a job during this time and had almost no savings left (fun fact, when I received my first payment in Melbourne, I'd left my Mexican bank account with less than 100 MXN or approx 5 USD).

Now it's been a similar story and I would say I am mostly at fault, since I knew that I had to be looking for positions and start filling up applications before finishing the PhD and I only did so after having submitted my thesis. Even then, it still took a little more than two months for the company to finish writing my contract (mind you, the institute is newly created, literally having started this year), then lunar year, and now the visa process, so a lot of it was out of my hands.

Now I can identify two (highly correlated) main sources of stress that are making me go insane: economic dependency and lacking real responsibilities. These are correlated because I can't really get one going without the other and more generally my life seems to be on hold until these two are clear. Also, it's quite strange because even though I am free to do whatever I want during this time, I don't feel quite free because I'm tied to this insolvency and the wait to get things going in Taiwan.

It's funny but during the PhD I became very square with regards to my schedules and I felt quite a lot of distress when the pandemic hit and I couldn't get on my day as usual. Now it's kind of the same, and even though I have a routine already during my stay in Mexico, it feels lack of a clear objective and overall sense. It's a tad ironic that having so much freedom actually can make you go insane. It reminds me of Camus' or other existential philosophers' discourses.

Anyhow, they say it gets darkest just before dawn, and I'm pretty sure I'm now seeing the end of it.

Missing out

It's been some 6 years now for me being away from home; while it's been rewarding in many regards, and I would absolutely not change it, it's been hard leaving people behind, or as I'm finding out now, reuniting with them, as they are not them anymore. And I don't mean this in a bad way, but simply that just as I made my life elsewhere and became someone else, so did they.

Now the most daunting prospect of moving once again is leaving a relationship behind and trying to keep it alive in long distance for a year. And I just realised that probably my biggest fear in this sense is simply that: missing out on her growth and evolution as a person and her missing out on mine, just not being there, becoming someone else. It is true that effective communication should go a long way, but even with my family I'm realising that even though I kept up to-date with most things, I still missed plenty of important moments: laughter, sadness, common struggle, dancing, face gestures, overall intrinsically sharing certain aspects of our view of life, etc. Then all the emotions that go with little things, that seemingly can only be shared by being alive there and then, together.

Then, for some reason my mind likes to play this futile game of filling up gaps, creating an artificial picture of things where I couldn't live through them; I suppose it's a way to create the illusion of understanding and empathy/connection with the other. This is mostly harmless to myself with family, but in the case of a special other it turns into a stinging feeling that can at times veer dangerously into insecurity and jealousy. On the other hand, how could you possibly accurately capture whatever is going on in your life, with all its richness (be it good or bad) without them living it there, locally in space-time, together with you?

I've been faced with the prospect of trying a long distance relationship before but at least in a couple there wasn't even a discussion, whereas with another we figure it would just not work and didn't deem it worth it. I feel like this time I approached things with much more naivety than I thought and that when people say it's hard they are implying many invisible but nevertheless pervasive hardships.

Fulfilment by Gustav Klimt

The art museum and the circus

I arrived in Melbourne in 2017 and I avoided the NGV (National Gallery of Victoria) for the most part of my stay. The NGV is an art museum and one of the iconic places at the heart of the city, right behind the famous Flinders Street Railway Station. I mostly avoided it because it strikes me as pretentious and lavish, generally not my type of place to experience art, even though historically art, just as science, has been almost exclusive for privileged people, it makes me uneasy whenever I perceive it to be treated that way (same with mathematics or science).

To be fair, and to start with the positive note, I did avoid the Gallery to my own detriment, as it does have some amazing pieces in its permanent collection. I did happen to visit, however, during a contemporary art exhibition called Triennial. I generally say I don't like contemporary art because the line between art and entertainment, between the deep and the banal, the everlasting and the immediate becomes too blurry for me. Now, the thing with the arts is that there is no true definition of what constitutes art and what does not; even if one can point to elements that must be present in a piece, like aesthetics, intelligence and technique, most of these are still subjective.

I do think, however, that the institutional display of most contemporary art (such as the one displayed at the Triennial) comes with a price for society at large. It seems like most people qualify any creative piece with an elevated sense of depth as art. These tend to be the same people that think that the act of reading should be fun, or that mathematics has value only if it can be applied; this is not to say that reading can't be fun or that applied mathematics are not valuable, but the act of reading is generally an intellectual exercise that should start a dialogue with the author that might face us with uncomfortable questions and make us think (which is largely a difficult and uncomfortable thing to do), and mathematics has a value in itself as the purest form of thought we know and perhaps the only way we have of defining and uncovering truth. It seems to me then that the price of such displays in art museums is a society that can't distinguish these from amusement parks, from circuses (circi?), from glossy instagrammable installations with flashy lights and/or colors. Now, similarly I don't intend to say that all contemporary is consumable fast food with no nutritional value, but rather that a large part of it is sold and perceived as something much more that what it actually is, bringing masses to institutional places selling mainly entertainment as artistic expression.

In the end, contemporary art does deserve a place and people with respective credentials should get to decide what gets displayed where; as things stand today, however, in many places it seems like the line between an art museum and an amusement park is quite hard to draw.

Porky Hefer at the NGV Triennial

On avoiding death

While these days back home I haven't been able to see friends and family for obvious reasons, at least I was able to see my grandma. She won't come out of her apartment almost for nothing, my mom takes care of most of the household chores, buying groceries and so on. And when she steps inside my grandma's apartment, she does so wearing a mask and a face shield; mind you, I proceeded in the same way.

In a sense, I guess in this situation we're all intentionally escaping death, either our own, someone else's, or both. And I guess we all go to different lengths to avoid it, we all give up something, some of us more and some of us less. What has surprised me the most during this pandemic is the selfishness of so many people in this regard, not understanding that them not giving up their normality can cost someone else's well-being or ultimately their life.

Overall, anyway, we all just seem to naturally want to perpetuate [our]  life at all costs. Even those aforementioned selfish bastards are laughing until they're not. As some people say, life's purpose seems to be simply to perpetuate itself and nothing else. That's perhaps the thing I find the most odd about suicide: it completely goes against the purpose of life whilst being the only true thing we have a power to choose (as opposed to everything in life, including to live). In a similar vein, I find as somewhat curious the joy that most people find in newborns or small kids, and how in a sense these result more valuable than older lives: a suicide of a middle aged person is intrinsically less tragic than that of a teenager.

These are just spare and somewhat disjoint thoughts on life and death that came to mind this morning and I felt like writing. As Albert Camus, I believe the one truly serious philosophical problem is suicide, and overall I tend to agree for the most part with Emil Cioran's thought that it's not worth the bother of killing yourself, since you always kill yourself too late.

Death And Life, 1908 by Gustav Klimt

Road cycling

It's been almost a month since I haven't ridden a (real road) bike. About a year and a half into my PhD I bought a road bike, influenced by a good friend of mine, and it totally changed my life and my perception of Melbourne, not to mention helping me stay afloat in some very dark days.

Even though I loved my bike and I actually invested quite a considerable amount in accessories and parts, I decided it was not worth it to carry it to Mexico and then to Taiwan. My plan is to get a road bike in Taipei asap when I get there; how quick I'll do this will depend on several factors.

I enjoyed my time riding in Melbourne and it's one of the things I will miss dearly. At first I'd always start riding at Clayton and my favourite routes would include taking the Scotchman's Creek trail to the city, riding on Beach Road, where I reached Mount Martha several times and climbed Arthur's Seat at least once, riding some of the climbs on the Dandenong Ranges like the "1/20" or "The Wall", doing some laps at Albert Park Lake, or taking the Yarra Boulevard for its sake or en route to other places such as Mount Pleasant road up in Research (yes, there's a suburb called that).

Melbourne was such an amazing place to ride in; I wish I could've ridden in other places in Australia as well, but I was busy doing my PhD. Anyhow, I'm now looking forward to riding in Taiwan; hopefully I'll be able to find a place where commutes to work will be nice and for sure I'll be eager to explore the country by bike whenever possible. There's also the famous Taiwan KOM Challenge, which I'd be happy to try in case it gets on during my time there.

La dificultad de llorar

Detesto el ardor en los ojos, el dolor de cabeza punzante, los sollozos en vaivén interminable. Detesto llorar no porque me haga patético, menos hombre o más maricón, sino porque me quiebra y me deja recogiendo pedazos de lo que soy, día tras noche.

 

Ojalá pudiese llorar con facilidad, y no me refiero a hallar motivos, sino al acto mismo de llorar: fortaleza la de poder llorar cuando se da la gana y no viceversa. Seguido me pregunto si los demás tienen la misma experiencia; no vale lo mismo llorar, por ejemplo, a causa de una película que por la muerte de un ser querido, pero hay quien llora igual por cualquiera de los dos y continúa su viaje temporal aparentemente como si nada, esa es una libertad que rara vez me he podido dar.

Aunque estoy lejos de estar orgulloso de mi dificultad para llorar, por otro lado tengo claros en mi mente los momentos en los que me he quebrado, todos cruciales, y siempre pegado a una almohada, llenándola no sólo de lágrimas sino también de mocos y saliva. La contrariedad es que éstos me recuerdan también los momentos en los que estaba obligado a llorar, no sólo porque así lo dictara un factor externo, sino por propia conciencia o porque era un reflejo natural del dolor que claramente sentía.

 

La mujer que llora, Pablo Picasso

Un año sin vesícula y sin perro

Hace poco más de un año me extirparon la vesícula biliar y un par de semanas después murió Gibson, un perro labrador al cual mi familia y yo quisimos mucho.

En cuanto a lo primero la cirugía fue lo más fácil del mundo, uno no se entera de absolutamente nada hasta que despierta y entonces sí empieza lo bueno: dolor durante alrededor de una semana y luego una paulatina recuperación; al final a uno le quedan cuatro cicatrices pequeñas en la barriga, que si uno tiene mala suerte (uno o más) pueden volverse una suerte de granos. También es triste que uno no puede hacer ejercicio de fuerza durante un tiempo pues se corre el riesgo de desarrollar una hernia abdominal. En mi caso pude regresar consistentemente al gimnasio por ahí de mayo o junio.

Sobre lo segundo, he tenido varios perros y con todos creo que he aprendido y mejorado algo en mi vida. Al final con cosas muy malas como una torsión gástrica que llevó a la muerte a uno de ellos y por lo cual siempre me culpé (nunca alimenten a su perro antes de sacarlo a jugar/correr), o varios extravíos, o reprimendas con golpes "por que así se enseñan"; con las que vinieron lecciones muy importantes que espero siempre tener presentes y jamás se me tengan que recordar.

Gibson apareció en mi vida en 2008 y a pesar de ser un perro labrador siempre fue miedoso y tímido, aunque ya una vez en confianza era muy juguetón. Conforme creció desarrolló las típicas conductas de territorialidad de ladrar en la puerta de la casa a todo extraño que se acercara o de mear cada rincón posible en todo lugar que visitara. Solía disfrutar enormemente salir a jugar y correr libremente en un cerro aledaño a nuestra casa y lamento no haberlo sacado más seguido. Varias veces lo dejé salir solo (algo que es común en México, que no por eso está bien), siempre seguía el mismo camino y siempre regresó a la casa... hasta que no lo hizo. Estuvo extraviado unos dos meses y lo encontramos de manera fortuita en una colonia cercana con una familia que lo adoptó y ya se había encariñado con él. Al final regresó con nosotros hasta que me fui a Edimburgo a estudiar la maestría y mi madre se hizo cargo de él. Alrededor de un año antes de morir desarrolló súbitamente un problema con su columna vertebral y luego de una cirugía y demás esfuerzos principalmente hechos por mi madre, pudo salvar su vida aunque sus patas traseras quedaron inmóviles. No sólo ésto, sino que tampoco tenía sensibilidad para orinar o defecar. Incluso cuando regresé de Edimburgo, aunque intenté ayudar en lo posible, mi madre se siguió haciendo cargo y desarrolló un especial afecto por Gibson. Poco antes de morir se le veía ya muy envejecido, quizá ya había señales de que su cuerpo no quería seguir más. Al final tuvo una muerte tranquila, mi madre empezó su rutina normalmente por la mañana, lo alimentó y lo dializó, luego salió por varios minutos y al regresar encontró al perro sin vida. Su voz se quebraba entre suspiros y llanto al hacerme saber lo que había ocurrido.

Es casi imposible explicar la conexión y marca que deja un perro u otro ser como aquél en nuestras vidas, o tratar de encapsularlo en una ínfima descripción. Siempre que pienso en esto recuerdo un párrafo de La insoportable levedad del ser de Kundera (al cual le siguen más reflexiones sobre la relación con los perros).

De la confusa mezcla de estas ocurrencias, crece ante Teresa una idea blasfema de la que no puede librarse: el amor que la une a Karenin es mejor que el que existe entre ella y Tomás. Mejor, no mayor. Teresa no quiere culpar a Tomás ni culparse a sí misma, no pretende afirmar que pudieran quererse más. Pero le da la impresión de que la pareja humana está hecha de tal manera que su amor es a priori de peor clase de la que puede ser (al menos en su caso, que es el mejor) el amor entre una persona y un perro, esa extravagancia en la historia del hombre, probablemente no planeada por el Creador.

Visto en Hobart, Tasmania (12/2017)

PhD en Australia, colecistectomía y la subaditividad de la entropía de von Neumann

Tres entradas en una 😉 Utiliza la lista expandible. Los dos primeros puntos tienen un carácter más personal pero igual con información que puede resultar útil.

1. PhD en Australia
En alrededor de un mes estaré en Melbourne, Australia para comenzar un PhD en el grupo de información cuántica de la Universidad de Monash (si no muero en la colecistectomía ☹️, ver punto 3). En Inglés, el nombre del grupo es Monash Quantum Information Science o MonQIS, que en el mismo idioma es homónimo de la palabra 'monkeys' que significa changos 🐵

El logo del grupo de información cuántica de la Universidad de Monash
El tema o problema específico que desarrollaré está por definirse pero lo más probable es que se trate de dinámica cuántica no-Markoviana (o al menos es el tema que más me atrae y que constituyó mi propuesta de investigación). Mi asesor principal será Kavan Modi, que aunque es relativamente joven, tiene ya una serie de contribuciones importantes al área.

A finales de la maestría ya estaba seguro de que no quería continuar en temas de altas energías y que me interesaba más la información cuántica o intentar en temas relacionados como teoría de probabilidad, procesos estocásticos, etcétera. Buscando proyectos disponibles encontré un anuncio de la Universidad de Monash sobre baterías cuánticas y decidí intentarlo. Cabe mencionar que no conocía la universidad ni tenía un interés particular por Australia; de cualquier modo todo resultó ser bastante bueno, la universidad, mi potencial supervisor y el país.

El proceso de admisión fue relativamente más sencillo que el de la maestría en Edimburgo, principalmente porque no requerí traducciones ni examen de idioma ni trámites de beca. El primer paso fue contactar al supervisor y—una vez que respondió—acordar una entrevista por Skype, que sí incluyó preguntas técnicas, comenzando por lo más básico—qué es la traza de una matriz cuadrada, cómo se calcula una traza parcial, qué es un producto tensorial, qué es un estado cuántico entrelazado— a otras más elaboradas, de las cuales no supe contestar para qué sirve el criterio de la transpuesta parcial positiva (o de Peres-Horodecki, luego me enteré). Sobreviviendo a la entrevista entonces el supervisor pide cartas de referencia, y una vez recibidas, envía una invitación formal para solicitar admisión a la universidad (sin ésta uno no puede comenzar el proceso). De aquí sigue el proceso estándar: subir documentación y esperar... y luego... seguir esperando.

Un punto importante es que al enviar la solicitud de admisión automáticamente uno es considerado como candidato para obtener apoyo financiero. Los tiempos de mi solicitud fueron:


Octubre	Envío de solicitud
Diciembre	Respuesta de financiamiento
Enero	Respuesta de admisión


Luego de esto ya sólo quedan los trámites estándar de inmigración. A propósito, el proceso de obtención de la visa de estudiante Australiana fue también bastante rápido y sencillo comparado con la gran jodienda de la visa de estudiante de Reino Unido. Quizá lo único pesado es que hay que llenar un formato bastante largo en línea pero luego de eso me dieron solución en algo así como una semana o bien algo como cinco o seis días hábiles. Otro detalle importante para Mexicanos es que la mayoría de vuelos a Australia pasan por Estados Unidos y es requisito (a diferencia de casi el resto de países del mundo) contar con alguna visa aún cuando sólo se vaya a hacer tránsito de algunas horas. La otra opción viable es buscar vuelos que pasen por Canadá (aunque luego hagan más escalas). Un dato curioso es que al parecer es más barato un vuelo México-Canadá-China-Singapur-Australia que uno idéntico sin pasar por Singapur aunque resulte más largo y por ende menos ecológico.

Quizá el proceso me resultó más sencillo porque ya tenía la experiencia de Edimburgo; como sea la larga espera fue el único calvario, intensificado por el hecho de que en el sitio de la universidad se promete dar una respuesta dentro de 6 semanas luego de la solicitud. Además de esto, durante la espera fui rechazado del Doctorado en Probabilidad y Estadística del CIMAT, donde se me dio la opción de hacer antes una especialidad de un año con el fin de regularizarme y poder enfrentar el doctorado. Las opciones que me quedaban eran intentar entrar a algún otro programa en verano, continuar con la propuesta de CIMAT o ya de plano intentar buscar trabajo y establecerme definitivamente en el país.

Como sea, por ahora ya tengo un plan de trabajo para los próximos tres años, luego ya la vida dirá 😎




2. Colecistectomía
Una colecistectomía es una extirpación quirúrgica de la vesícula biliar y el día de mañana me toca someterme a una.

En resumidas cuentas, en el año 2011 se me detectó incidentalmente, en un estudio de ultrasonido, un pólipo de 5mm de diámetro en la vesícula biliar e indicios de lodo vesicular (básicamente pequeños gránulos de bilis), luego hace un par de meses, también incidentalmente, se vio que el pólipo había aumentado su tamaño al doble y que en lugar de gránulos tengo ya pequeñas piedras biliares formadas.

Vale, no soy médico así que no daré mucho detalle, aunque igual aprendí varias cosillas (que de hecho debí haber aprendido desde el bachillerato).

La vesícula biliar es un pequeño órgano con forma de pera alargada que está situado del lado derecho del abdomen a la media altura de las costillas, además de estar adherido al hígado; su función es básicamente guardar una sustancia llamada bilis—producida por el hígado—que permite la digestión de grasas, liberándola una vez que éstas son ingeridas.





En este tan preciso diagrama se observa la vesícula en color verde reteniendo cálculos de bilis


Las causas tanto de los pólipos como de los cálculos biliares al parecer son poco claras y sólo se identifican factores de riesgo como ser mujer, tener sobrepeso u obesidad, tener más de 40 años o la propia genética. Usualmente las piedras y los pólipos están constituidos principalmente por colesterol y triglicéridos.




El trabajo de la vesícula es sencillo pero igual lo puede arruinar


En general, ni el pólipo ni las pequeñas piedras me han manifestado síntomas (directos), aunque en mi caso el mayor problema lo puede representar el pólipo y su crecimiento descontrolado, ya que en un futuro puede convertirse en cáncer, que a su vez puede extenderse a otras zonas. En cuanto a los cálculos, el problema es que éstos pueden salir de la vesícula luego de una comida grasosa (como casi no nos gustan a los Mexicanos) y atorarse en un conducto o en general provocando problemas en otros lados. En mi caso luego de una endoscopía con biopsias se me diagnosticó con gastritis química y esofagitis, básicamente provocadas por la misma bilis. Así que al final todo se vuelve un lío.




De los problemas más graves que pueden causar las piedras biliares está la pancreatitis


Al final igual parece demasiado tener que extirpar a la pobre vesícula pero parece ser lo más sensato, pues luego no parece haber garantía de que los cálculos o el pólipo mismo no regresen, además de que presuntamente los tratamientos para eliminarlos son costosos y elaborados. La colecistectomía más usual hoy en día es la de tipo laparoscópico, que es un procedimiento mínimamente invasivo para acceder a los órganos y hacer las manipulaciones necesarias. Básicamente se hace una serie de incisiones en puntos bien determinados por las que se insertan unos tubos que permiten ver y manipular los órganos.




Diferencia entre colecistectomía laparoscópica y abierta; la segunda actualmente se realiza sólo en casos excepcionales


En YouTube hay vídeos con el procedimiento completo y a mí incluso me entregarán uno con mi cirugía 😎 (tanta emoción!). Un detalle un tanto escalofriante es que usualmente cierran dos conductos (por el que pasa la bilis y una arteria) con unos pequeños clips de titanio y al final éstos se le quedan a uno ahí como si nada 😨 Como sea, espero que todo vaya bien y que pueda llegar sin mayor problema a la land down under para el PhD.




Afortunadamente mi vesícula no será ni linda ni popular, así que no hará falta una colecistectomía inversa 😉

3. Subaditividad de la entropía de von Neumann
Antes de empezar el PhD he estado tratando de aceitar mi cabeza con las cosas básicas que debo saber. Revisando mis notas de mi curso de información cuántica de la maestría di con lo siguiente.

La entropía de von Neumann para un sistema cuántico descrito por una matriz de densidad $\rho$ está definida por \begin{equation}S(\rho)=-\mathrm{tr}(\rho\ln\rho)\end{equation} Al considerar un sistema compuesto $\mathcal{H}_A\otimes\mathcal{H}_B$ descrito por $\rho^{AB}$, se satisface \begin{equation}S(\rho^{AB})\leq{S}(\rho^A)+S(\rho^B)\label{subadd}\end{equation} donde $\rho^A=\mathrm{tr}_B(\rho^{AB})$ y $\rho^B=\mathrm{tr}_A(\rho^{AB})$ son las matrices reducidas. Esto se conoce como propiedad de subaditividad. Para mostrar que $S$ en efecto tiene esta propiedad, antes se puede usar la definición \begin{equation}S(\rho\|\sigma)\equiv-S(\rho)-\mathrm{tr}(\rho\ln\sigma)\end{equation} que satisface $S(\rho\|\sigma)\geq0$, que a su vez se puede mostrar definiendo $\rho=\sum_ip_i|i\rangle\langle{i}|$, $\sigma=\sum_jr_j|j\rangle\langle{j}|$ y llegando luego a que $S(\rho\|\sigma)\geq{D}(p_i\|r_j)=\sum_ip_i\ln\frac{p_i}{r_i}$, donde el lado derecho es entropía condicional clásica (base nat) que se sabe es positiva o nula.

Vale, a lo que voy es que con esto, que implica $S(\rho^{AB}\|\rho^A\otimes\rho^B)\geq0$, se puede decir (o concretamente, se dice en mis notas de la maestría) en una línea que \begin{equation}S(\rho^{AB})\leq-\mathrm{tr}\left[\rho^{AB}\ln(\rho^A\otimes\rho^B)\right]=-\mathrm{tr}\left[\rho^{AB}(\ln\rho^A+\ln\rho^B)\right]=S(\rho^A)+S(\rho^B)\end{equation} y (\ref{subadd}) queda demostrado.

El detalle es que hay varios pasos que no se ven muy claros. Primero, debe ser evidente que \begin{equation}\rho^{AB}(\ln\rho^A+\ln\rho^B)\equiv\rho^{AB}(\ln\rho^A\otimes{I}^B+I^A\otimes\ln\rho^B)\end{equation} donde $I$ son identidades, que es un pasillo inocentón hasta cierto punto, ya que \begin{equation}\ln(\rho^A\otimes\rho^B)=\ln\rho^A\otimes{I}^B+\rho^A\otimes\ln{I}^B+\ln{I}^A\otimes\rho^B+I^A\otimes\ln\rho^B\end{equation} y por supuesto $\ln{I}=0$ dado que $e^0=I$ por definición, además $X\otimes{0}=0\otimes{X}=0$, así que realmente sólo se busca ahorrar notación. Como sea, la última igualdad no parece tan evidente, dado que por definición \begin{equation}S(\rho^A)=\mathrm{tr}_A(\rho^A\ln\rho^A)\end{equation} Vale, la igualdad, explícitamente, se sigue de la siguiente manera: \begin{align}\mathrm{tr}[\rho^{AB}(\ln\rho^A\otimes{I}^B)]&=\mathrm{tr}_A\left\{\mathrm{tr}_B\left[\rho^{AB}(\ln\rho^A\otimes{I}^B)\right]\right\}\label{p1}\\ &=\mathrm{tr}_A\left\{\mathrm{tr}_B\left[\rho^{AB}(I^A\otimes{I}^B)\right]\ln\rho^A\right\}\label{p2}\\ &=\mathrm{tr}_A\left[\mathrm{tr}_B\left(\rho^{AB}\right)\ln\rho^A\right]\\ &=\mathrm{tr}_A(\rho^A\ln\rho^A)\end{align} y de forma similar para $S(\rho^B)$. De aquí los dos pasos importantes son (\ref{p1}) y (\ref{p2}): el primero afirma que \begin{equation}\mathrm{tr}(X^{AB})=\mathrm{tr}_A[\mathrm{tr}_B(X^{AB})]=\mathrm{tr}_B[\mathrm{tr}_A(X^{AB})]\end{equation} y en efecto, si $\{|a_i\rangle\}_A$, $\{|b_j\rangle\}_B$ son bases de $\mathcal{H}_A$ y $\mathcal{H}_B$, respectivamente, se sigue (explícitamente) que \begin{align}\mathrm{tr}(X^{AB})&=\sum_i\sum_j\left(\langle{a}_i|\otimes\langle{b}_j|\right)X^{AB}\left(|a_i\rangle\otimes|b_j\rangle\right)\nonumber\\ &=\mathrm{tr}_A[\sum_j\left(I^A\otimes\langle{b}_j|\right)X^{AB}\left(I^A\otimes|b_j\rangle\right)]\nonumber\\ &=\mathrm{tr}_A[\mathrm{tr}_B(X^{AB})]\\ &=\sum_j\sum_i\left(\langle{a}_i|\otimes\langle{b}_j|\right)X^{AB}\left(|a_i\rangle\otimes|b_j\rangle\right)\nonumber\\ &=\mathrm{tr}_B[\sum_i\left(\langle{a}_i|\otimes{I}^B\right)X^{AB}\left(|a_i\rangle\otimes{I}^B\right)]\nonumber\\ &=\mathrm{tr}_B[\mathrm{tr}_A(X^{AB})]\end{align} De manera similar, para la segunda, de la misma definición de la traza parcial, \begin{align}\mathrm{tr}_A\{\mathrm{tr}_B\left[X^{AB}(Y^A\otimes{I}^B)\right]\}&=\mathrm{tr}_A\{\sum_j\left[(I^A\otimes\langle{b}_j|)X^{AB}(Y^A\otimes{I}^B)(I^A\otimes|b_j\rangle)\right]\}\nonumber\\ &=\mathrm{tr}_A\{\sum_j\left[(I^A\otimes\langle{b}_j|)X^{AB}(I^A\otimes|b_j\rangle)\right]Y^A\}\nonumber\\ &=\mathrm{tr}_A\left[\mathrm{tr}_B(X^{AB})Y^A\right]\end{align} que funciona de manera similar con $\mathrm{tr}_B\left\{\mathrm{tr}_A\left[X^{AB}(I^A\otimes{Y}^B)\right]\right\}$.

En efecto esto no se escribe explícitamente la mayoría del tiempo y prácticamente siempre se omiten productos tensoriales con identidades; como sea vale la pena destripar todas estas expresiones si se quiere entender realmente cómo está funcionando todo.