In the past year I had the pleasure of reading two popular science books about topics that are very close to my heart. Lee Smolin’s “The trouble with physics” and Vlatko Vedral’s “Decoding reality”. Both are excellent scientists and science communicators and the books are highly recommended.
After a long an eventful month that included a visit by Kavan Modi to IQC and my visit to Israel (I’m posting from Israel), it’s time I got back to writing something. This time I’ll say something about my work for the past four years (as promised). One of the main subjects of my research is quantum correlations, and their role in defining the difference between quantum and classical (not quantum) systems.
Imagine a piece of information shared between two people Alice and Bob. Now think of a way to quantify the correlations between them. One way to quantify correlations is to ask what can Alice know about Bob’s part of the information by looking at her own part.
For example lets say Alice and Bob are each given a queen from a chess board. Alice then looks at her queen and sees it is white. She now knows Bob’s queen must be black. Alice and Bob are strongly correlated, since Alice always knows Bob’s piece by looking at her own.
For the second example Alice and Bob are each given a queen, but this time from a Deck of cards. If Alice sees a red queen she can say that it is more likely that Bob has a black queen, but she has no certainty. Correlations are lower in this case then in the chess example.
There is another way to account for correlations. We can ask about difference between the information in Alice and Bob’s hands individually and the information in their hands together. In the chess example Alice and Bob can each get one of two types of queens: black or white Together they also have two options Black White or White Black.
It turns out that both options for quantifying correlations are the same. To see this in the example we need to quantify the information in bits. Since Bob has two options in his hand “black queen” or “white queen” he has one bit of information. The amount of information Alice can discover about Bob is precisely this one bit. So they have one bit of correlations. Alternatively we can say that Alice has one bit of information: “black queen” or “white queen”; Bob has one bit of information: “black queen” or “white queen” and together they also have one bit “black white” or “white black”. The difference (1+1)-1 is again 1 bit so there is one bit of correlations.
Since i’m avoiding maths you will have to take my word that both methods give the same result in all cases… in the classical world. In the quantum world things are a bit different.
There are two essential (and related) aspects of quantum theory that make these two ideas about how to to quantify correlations give different results. 1) Measurements affect the system. If Alice wants to know the color of her queen, she needs to make a measurement, this measurement can change the state of the system; and 2) Quantum systems can be correlated in a much stronger way then classical systems, a phenomenon known as entanglement.
Before discussing the first aspect in detail, I will say a bit about entanglement. Entanglement was a term coined by Schrodinger in his famous “cat” paper, this paper was inspired by the earlier “paradox” of Einstein Podolski and Rosen (EPR). They showed that quantum mechanics predicts a situation where a system shared by two parties is in a well defined state although locally it is not defined. A system is in a well defined state if making a measurement on this system will give some result with certainty. So if I give Alice and Bob an entangled system I can predict the result of a measurement made on the whole system, but I cannot predict the result of a measurement made by Alice and Bob separately.
Entanglement is the most remarkable prediction of quantum mechanics, and in one way of another it is the driving force behind most of the really cool quantum phenomena. From quantum computers to Schrodinger’s cat. Nevertheless entanglement does not account for all the non-classical features of the theory. At least not directly. When discussing correlations, measurements and their effects on the system play a crucial role in describing non-classicality. To explain quantum measurements we can imagine a quantum system as an arrow pointing to some direction, X, in the simplest case we can think of this problem in two dimensions.
A quantum measurement is a question regarding the direction of the arrow. Is the arrow pointing in direction A? This has one of two results either yes or no. The probability is given by the angle between the “actual” direction and the direction in question. The effect of the measurement is that the arrow will now point in the same direction as the result. If the answer is yes it will point in direction A if the answer is no, it will point in the opposite direction.
Ok so what does this have to do with correlations? Well lets go back to the two definitions for correlations. The first was “What information can Alice find about Bob by looking at her own system”. In the quantum case this is no a clear question, we need to also say what measurement Alice is making. Different measurements will reveal different information about Bob. The second definition for correlations is what is the difference between the information in Alice’s hands plus the information in Bob’s hands and the information in their joint system” This is not directly related to measurement, so clearly it is not the same as the first definition. The difference between these definitions in the quantum case is the quantum discord. It is a measure of the “quantumness” of correlations.
As it turns out discord can be found in many interesting quantum systems and paradigms, but it is not yet clear what this means…
Two expected, but long awaited events happened on my birthday. One: I found out that my Phd was approved, so no more bureaucratic shit regarding that. Two: The review paper on discord and similar quantities was finally published. This sums up about one and a half years’ work spent on reading, writing and rewriting this review with my collaborators. Two versions have been posted on arXiv since the end of last year. The latest one, posted in August, is pretty much the published version.
I will soon post something longer about discord and non-classical correlations, for now it is enough to say that quantum theory allows more general correlations then a classical theory. Entanglement is the best example of these types of correlations, but as it turns out there are unentangled systems with non-classical correlations. Quantum discord captures entanglement and more (but not everything).
Since the beginning of the century (i.e 12 years ago) people started studying these kinds of correlations “beyond” entanglement in various forms and physical scenarios. The area exploded about 5 years ago and discord became a “hot” topic. The review includes almost all the work done on the subject until the end of 2011. discord was studied in so many different scenarios like quantum information, thermodynamics, many body systems, relativistic quantum information and others which made work on this review so much fun, on the one hand, but a lot of work on the other.
In good time for my 33rd birthday The Wiki Religion was resurrected. After being martyred by the vast evil community of spammers, the wiki rose from the ashes of no-host and no-domain back to the land of the online.
All should drink and rejoice to our great prophet Kaer.fyzarc may his booze ever remain strong.
In case you want to put your money where your mouth is on future predictions, this website lets you bet on a whole bunch of weird shit, from finding supersymmetric particles before the end of this or next year and the discovery of extraterrestrial life to the amount of snow in central park.
They give a 1% chance that Hamas will recognize Israel before Midnight december 2012 a 6% chance that the US or Israel will attack Iran before the end of the year and a 49% chance it will happen before the end of next year.
A cool new paper appeared in Nature Physics this week and made a lot of waves (at least on my facebook feed).
In this paper titled “Quantum non-locality based on finite-speed causal influences leads to superluminal signalling” the authors show a method for testing if the “weird” effects of entanglement such as the violation of Bell inequalities can be explained using a faster then light source for exchanging information.
The main problem with these kinds of theories is that the usual Bell experiments can at best put a lower bound on the speed of exchanging this kind of information. The way to overcome this problem is to look at Bell violations in a 4 party system. The result of the paper is that one can perform a test that requires the speed of these causal influences to be infinite.
The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland “for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems”.
Still taking a long time between posts. Mom and Dad were here for the past two weeks, and we finally did some traveling. Canadian Autumn is absolutely amazing.
Too much writing at uni has taken its toll. But in the interest of keeping this blog alive here’s an email Mauro wrote me in January titled “Heavy Metal Universe!” in an attempt to enhance my knowledge of heavy metal. Cynic’s first album has been on my playlist since then so cheers Mauro.
Anyway, here it is in full, Mauro’s Heavy Metal Universe, enjoy
– The fathers of Death Metal:
– Old School Death Metal:
– Doom Metal:
– Brutal Death Metal:
– Death/Black Metal:
– Crazy Stuff:
– A Thrash Gem!:
– …the Joy in the Heavy Metal Universe!:
Busy days but not much interesting going on. Computer crashed, enjoyed the last (long) weekend of summer and got drunk Saturday night. Not much to write about.
Guess its time to start digging into some old insights about the human condition. On today’s menu is The Spectrum of Indubitability. This particular gem of our quantum kitchen discussions was a result of the ongoing debate on the merits of the global warming scene. My argument that the term “consensus” used too loosely when compared with the consensus regarding other scientific theories such as quantum mechanics, evolution, relativity and Newtonian mechanics led to Thorn plotting various theories and psudo-theories on a graph he aptly named The Spectrum of Indubitability.
Note that The Wiki Religion was placed between quantum mechanics and 2+2=4.