# Quantum Bayesian Networks

## September 30, 2012

### Weak Measurements Remind me of…

Filed under: Uncategorized — rrtucci @ 11:22 pm

I hate to say it but weak measurements remind me of homeopathy. It would be nice if someone did an experiment that measured the “same” quantity with a non-weak and a weak measurement, and compared the two results. Or are we to believe that weak measurements allow us to access parameters which non-weak measurements cannot access? But that would be a hidden variables theory, or something that went beyond standard quantum mechanics, wouldn’t it. I don’t have time to think about this any further because I’m working on something else and my time is limited, but I hope others will.

My previous post on Weak Values:

Dull Measurements (aka Weak Measurements)

Advertisements

### Parlez-vous Thermodynamique?

Filed under: Uncategorized — rrtucci @ 6:22 am

I’ve preached a lot in this blog about SIT (Shannon Information Theory). The problem with pure SIT is that is says nothing about energies. And living without being able to talk about energies is an unbearably cruel fate for a physicist. But, what’s this…Ta,tan…Thermodynamics to the rescue. According to Thermodynamics, temperature is defined as $T = \frac{dQ}{dS}$, a change in energy divided by a change in information (information = entropy, probability spread).

One of my future goals is to make QB nets (quantum Bayesian networks) speak the language of thermodynamics. What is the connection between the two?, you might ask.

In my previous papers, I showed how QB nets can be used to represent quantum density matrices. Suppose that we consider a protocol described by a density matrix $\rho(t)$ that evolves as function of time $t$. Suppose at time zero, $\rho(0)$ is a tensor product of several density matrices, one of which is the thermal (aka Gibbs or Boltzmann, or canonical ensemble) density matrix $\exp(-\beta H)/Z$, where $H$ is a Hamiltonian operator, $\beta$ is a positive real number and $Z= tr(e^{-\beta H})$. Also $\beta = \frac{1}{k_B T}$ where $k_B$ is Boltzmann’s constant and $T$ is the temperature of the system whose Hamiltonian is $H$. Since there is a “thermal density matrix” in such a protocol, the “thermal” part beckons Thermodynamics and the “density matrix” part beckons QB nets.

QB nets are also an ideal vehicle for representing measurement theory in quantum mechanics. If you combine Thermodynamics, QB nets and outlandish measurements, you immediately find yourself wandering into the territory of Maxwell demons.

I think Maxwell demonology is a great gedanken experiment on which to improve my knowledge about the nether world of QB nets and thermo. So next month (appropriately enough, Halloween month), I will dedicate myself to trying to translate some of the already existing Maxwell demonology protocols to the language of QB nets. And thus make Reverend Bayes preach about Maxwell demons, hell, brimstone and thermodynamics. Maybe at the end of this fun project, I’ll write a pedagogical paper with my ruminations.

I don’t expect that during the course of this project, I will discover anything fundamentally new that hasn’t been discovered and written about by others many times before. Although the subject of Maxwell demonology was viewed with much fear and bewilderment in the past, my impression is that since Maxwell’s time, significant inroads have been made into understanding the subject and it is nowadays considered fairly well understood and settled.

Truly, I will be standing on the shoulders of giants for this project. Maxwell demonology has a vast and illustrious history in Physics. Here are some of the more famous tracts on these dark arts

J. C. Maxwell, “Theory of Heat” (Appleton, London, 1871).
L. Szilard, Z. Phys. 53, 840 (1929).
L. Brillouin, J. Appl. Phys. 22, 334 (1951).
R. Landauer, IBM J. Res. Develop. 5, 183 (1961).
C. H. Bennett, Int. J. Theor. Phys. 21, 905 (1982).
R. Landauer, Science 272, 1914 (1996).

In the past 5 years or so, a Japanese school led by Sagawa and Ueda has come out with some fine papers which are the culmination and synthesis of much previous work by others and some new one by them. These papers, to my mind, have exorcised Maxwell’s demon, at least for a long while. For example, here is one paper by them that I like very much:

“Minimal Energy Cost of Thermodynamic Information Processing: Measurement and Information Erasure”, by Takahiro Sagawa and Masahito Ueda
arxiv 0809.4098v3

## September 14, 2012

### Dull Measurements (aka Weak Measurements)

Filed under: Uncategorized — rrtucci @ 5:53 am

Let me start by warning the reader that the terms  “weak measurements” and “weak values” are both misnomers. It’s difficult to understand how the adjective “weak” can apply to the noun “measurement”. And the values involved can be very large (even infinite), which is not very weak.

Instead, I like to call them dull measurements (dull Ms), because they have a very large variance (The name dull M also fits well because, once one understands what dull Ms are, talking further about them makes any honest physicist incredibly bored.)

Besides Dull Measurements, other useful names for them are dumb measurements, BS measurements, almost fake measurements, fuzzy-wuzzy measurements, …

Dull Ms consist of a weak INTERACTION (not weak measurement) between two systems, call them S and M, followed by a measurement of M. S is usually called the system and M the meter or pointer or ancilla. S can be taken to be microscopic and M macroscopic, but that’s not necessary. It’s common to use the symbol $\langle A \rangle_W$ to denote the so called weak value of an operator $A$ for the initial state $|\psi_i\rangle$ and final state $|\psi_f\rangle$

$\langle A \rangle_W = \frac{\langle\psi_f |A| \psi_i\rangle} {\langle\psi_f |\psi_i\rangle}$

If you are interested in a short, more mathematical discussion of dull Ms, I’ve written one which you can find here. It’s just 2 pages long.

• Do dull Ms constitute new or fundamental physics?  Absolutely not. Dull M proponents try to extend, in a dubious way, some theory that was first proposed eons ago, by von Neumann and others. The physics and math necessary to understand dull Ms is standard, VERY BASIC, quantum mechanics, the stuff taught in a beginning quantum mechanics course. It’s that trivial.

It’s really important to face the truth: the effects called “weak measurements” can all be explained by standard quantum mechanics. No modifications of standard quantum mechanics are required to explain them.

• Will the study of dull Ms lead to new, useful technological applications, like, for instance, improvements in precision metrology? Very unlikely. Dull Ms are very noisy measurements. Usually, improvements in precision metrology arise from discoveries of new ways of reducing noise, not of increasing it.
• Do dull Ms violate Heisenberg’s uncertainty principle, as claimed by people like Aephraim Steinberg? Absolutely not. Heisenberg’s uncertainty principle for momentum and position (or any other conjugate pair of variables) is a simple application of the Cauchy-Schwarz inequality. So according to Aephraim Steinberg, he has found a way of violating the Cauchy-Schwarz inequality. Don’t laugh.

The familiar Heisenberg uncertainty principle refers to measuring $p$ on one particle and $x$ separately on a second particle that is prepared identically to the first. Steinberg, following a theoretical calculation by Ozawa, is measuring $p$ and $x$, one after the other, on the same particle. The fact that these two situations obey different uncertainty principles has been known since the early days of quantum mechanics.

As evinced by many quotes of him that have appeared in news articles, Mr. Steinberg is in the habit of telling the press that his work is super revolutionary, that it will rewrite the physics books, that most physicists did not expect this or thought it to be outright false, that he has found a violation of a cherished principle of physics. Then you go to his papers. There he chooses his words a bit more carefully. There he only claims to have checked a fairly standard prediction of standard quantum mechanics. One is reminded of the bait and switch sales scheme, and of the Roman god Janus, guardian of doorways, two-faced.

• Are dull Ms always well defined? Sometimes they aren’t, as has been pointed out by Stephen Parrott and others. Let me try to explain this.

(1)Dull M theory is ONLY VALID TO FIRST ORDER in an expansion parameter (also called a coupling constant) $g$. That’s why it’s called a weak measurement. Hence, dull M theory is invalid for large $g$.

(2)Dull M proponents always find equations that give $\langle A \rangle_W$ in terms of actual lab measurements. The problem is that in those equations, $\langle A \rangle_W$ and $g$ always appear together, as a product $g\langle A \rangle_W$. So when $g=0$, all information about $\langle A \rangle_W$ goes away. $\langle A \rangle_W$ is a random variable whose variance is infinite when $g=0$. That variance is finite but still very large when $g\in (0,\epsilon]$ for some $\epsilon \neq 0$.

(1) and (2) imply that dull M theory is vacuous for small $g$ and invalid for large $g$. It ONLY WORKS FOR INTERMEDIATE VALUES OF $g$. This poorly defined region of intermediate $g$ values may be the empty set.

• But aren’t there alternative definitions of $\langle A \rangle_W$ which are not based on an ill defined approximation? Some people like Johansen have given “interpretations” of  $\langle A \rangle_W$ based on Bayesian estimation.

It’s easy to explain what Johansen is saying. Suppose you are given a Hermitian matrix $A$ and a fixed orthonormal basis $|b\rangle$ for all $b$. Then suppose you want to find a Hermitian matrix $\theta$, called an estimate of $A$, which is diagonal in the $|b\rangle$ basis. Thus, it can be expressed as $\theta = \sum_b \theta_b |b\rangle\langle b|$. $\theta$ should be as close as possible to $A$. Close as possible is defined as minimizing $L=\langle \psi|(\theta-A)^2|\psi\rangle$ for some state $|\psi\rangle$. Then some math shows that the best estimate is $\theta_b = Re\left(\frac{\langle \psi|A|b\rangle}{\langle \psi|b\rangle}\right)$.

Fine. But such an interpretation has nothing to do with an experiment that yields $\langle A \rangle_W$ from a weak interaction. In fact, such an interpretation totally avoids a coupling constant $g$ because it doesn’t consider any sort of interaction, whether a weak one or a strong one. Such an interpretation is quite different to what most people call a “weak measurement” experiment.

• Are weak measurement skeptics rare? No. It seems that there are quite a few, including some famous people. For example, I already mentioned Stephen Parrott. Anthony Leggett has also expressed some misgivings about weak measurements in a lecture which can be found on You Tube. Lubos Motl, who knows a lot of physics, thinks they are total rubbish.

Wikipedia entry for weak measurements here. Notice flag questioning neutrality of article.

Lies, Damn Lies and Hilariously Dishonest Hype about dull Ms.

• Check out

“Can apparent superluminal neutrino speeds be explained as a quantum weak measurement?” by M V Berry, N Brunner, S Popescu and P Shukla.
J. Phys. A: Math. Theor. 44, 492001 (2011)
Received 12 October 2011,
Published 11 November 2011
(arxiv 1110.2832)

If you skim this paper, you will find that it was not intended as a joke. It has a very serious tone, except maybe for the abstract. Notice that the journal “Journal of Physics A: Mathematical and Theoretical” published this embarrassing nonsense just one month after it was submitted. According to Wikipedia, the Journal of Physics A is run by IOP, which is a UK institution whose current president is the unsavory character, Peter Knight. (I once had a very unpleasant experience with this guy. I suspect I’m not the only one that dislikes him.)

• Check out

“Heisenberg uncertainty principle stressed in new test” Pioneering experiments have cast doubt on a founding idea of the branch of physics called quantum mechanics. , by Jason Palmer, BBC news, September 7, 2012

which extolls the virtues of the paper

“Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements.” by Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, and Aephraim M. Steinberg (arxiv 1208.0034)

• (for adults only) Lubos Motl’s reaction to Steinberg’s paper “Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements.”

Pseudoscience hiding behind “weak measurements”

• The magazine PhysicsWorld, also published by IOP, recently published a hilariously biased “contest”. Check it out

Physics World reveals its top 10 breakthroughs for 2011

The “Physics World editorial team” awarded 10 prizes. First and second prizes were awarded to weak measurement experiments. The output of such crap experiments is just a very noisy, washed-out interference pattern. Real useful and novel, for a caveman, that is. On the other hand, Cleland’s and Martinis’ quantum computer with RAM, which I think is truly revolutionary, only rated ninth prize. Sigh…the English.

The article says about Steinberg’s team, which won the first prize:

“…the team is the first to track the average paths of single photons passing through a Young’s double-slit experiment – something that Steinberg says physicists had been “brainwashed” into thinking is impossible.”

What BS! Mr. Steinberg. Stop lying. Physicists are taught that one can only “estimate” those paths with very high variance. What are the variances in your crap experiment? They’re huge.

• Dull Ms were originally promoted by Yakir Aharonov, David Albert and Lev Vaidman. AAV used dull Ms in their crackpot interpretation of quantum mechanics called 2 state-vector formalism (2S). According to AAV, particles have two parts: one part lives in the present and another in the future; these 2 parts send encrypted messages to each other. LOL. The 2S interpretation generated a lot of heated debate in PhysicsToday in 2011. More recently, one finds the following priceless blog post

Physics World gets high on Tel Aviv catnip
by Charles Bennett

in which Charles Bennett comments on an over-exuberant article (in the magazine IOP-PhysicsWorld) about the 2S interpretation.

Update: A more recent post of mine on dull Ms:

Weak Measurements Remind Me of…

## September 7, 2012

### Of Balloons and Steel Balls

Filed under: Uncategorized — rrtucci @ 7:26 pm

Yesterday I listened on the radio to many great speeches being delivered at the DNC (Democratic National Convention). Furthermore, as you may have gathered from my previous blog posts, recently I’ve been obsessively interested in SIT (Shannon Information Theory)—to the point that I’m beginning to see SIT in everything, even in the DNC. In both SIT and the DNC, there are sender nodes and receiver nodes. The receiver nodes in turn become sender nodes themselves.

I like to think of SIT as the study of a special type of bayesian network. The bayesian networks of SIT have nodes of two kinds: one kind of node stores “messages”; the other kind stores “codewords”. Codeword nodes are like helium filled balloons; they don’t store information in a very high density format. On the other hand, message nodes are like steel balls; they are small, compact, dense storers of information.

The main two problems of SIT were first proposed and completely solved by Shannon in his 1948 paper. They are Source Coding and Channel Coding. Both problems can be represented by Bayesian networks (as can all other problems in SIT, and in the universe, as far as I’m concerned). Here is how I portray these two problems in my paper “Shannon Information Theory without Shedding Tears over Delta & Epsilon Proofs or Typical Sequences

In this figure, random variables are denoted by underlining. “Codewords” are denoted by a letter raised to the n’th power, like $\underline{x}^n$. Estimates of a quantity are denoted by that quantity with a hat over it; for example, $\widehat{\underline{m}}$ is an estimate of $\underline{m}$.

Notice that in source coding, the information density goes from low to high to low again. The high density is in the middle. For channel coding, it’s the opposite. Information density goes from high to low to high again. The low density is in the middle.

P.S. I find that writing this blog is very useful to me. For one thing, it helps me to organize my ideas. Blogging reminds me of a quote I read recently:

“The art of writing is the art of discovering what you believe.” Gustave Flaubert

## September 1, 2012

### RSA Easily Breakable by CIA or Chinese Gov. 5 Years From Now?

Filed under: Uncategorized — rrtucci @ 12:22 pm

The Cleland and Martinis groups at UCSB have struck pay-dirt again (see Refs. below). This time they have used their QC made with superconducting qubits to factor 15=3X5 using Shor’s algorithm. Furthermore, they believe they have a clear road map for scaling up the size of their device so that it can factor larger numbers. And so far they have a very good track record of doing what they’ve promised.

RSA cryptography, which is based on factoring numbers, is the most common kind of cryptography used for commerce on the Internet. RSA is almost impossible to break with classical computers, but could be easily broken by a UCSB type device, if such devices can be scaled up.

There are certain types of classical cryptographies, called post-quantum cryptographies, which cannot be easily broken by QCs, as far as we know. Some are already available, although not yet in a convenient form.

In theory, switching from RSA to post-quantum crypto should be possible long before QCs arrive. But one shouldn’t forget human inertia. World history is full of examples of situations (Maginot Line, Hurricane Katrina, building whole cities on flood zones, fault zones, and next to volcanoes, etc., etc.) in which societies and their governments took too long to react to an approaching danger, or reacted inadequately to it. It’s likely that some mismanaged institutions and some people that are naive or ignorant or careless or prone to procrastination will continue to use legacy RSA code, long after a cheap and convenient post-quantum substitute is available.

References

• “Computing prime factors with a Josephson phase qubit quantum processor” by
Erik Lucero, Rami Barends, Yu Chen, Julian Kelly, Matteo Mariantoni, Anthony Megrant, Peter O’Malley, Daniel Sank, Amit Vainsencher, James Wenner, Ted White, Yi Yin, Andrew N. Cleland, John M. Martinis arXiv:1202.5707, published in Nature Physics (19 August 2012).

Another source of information about the same experiment is Erik Lucero’s Ph.D. thesis, which can be found at Prof. Martinis’ excellent website. Lucero has been hired as a postdoc by the group led by Matthias Steffen at IBM, a group which is working on a QC architecture based on superconducting qubits, similar to the UCSB one.

• Previous posts in this blog about the Martinis and Cleland groups at UCSB

• good news for quantum computing?, post by aram at “Quantum Pontiff” blog

Blog at WordPress.com.