Tuesday, March 9, 2010

Adán Cabello's Big Deviation From Classicality

Quantum mechanics is the most successful theory of the material world that humans have ever possessed. It makes accurate predictions to eleven decimal places and wherever it's been tested IT HAS NEVER BEEN WRONG. But the price we seem to have paid for quantum theory's immense predictive power is an utter inability to visualize quantum reality. Whenever we make a measurement the unvisualizable quantum world turns into solid, visualizable matter--the so-called "classical world" of Newton and Galileo.

In my book on this topic I compare our inability to directly perceive the world's underlying quantum reality to King Midas's touch. King Midas cannot enjoy the touch of his daughter's hand because everything he touches turns to gold. Humans cannot directly perceive quantum reality because everything we touch turns to matter.

In the last quarter century, inspired by Irish physicist John Bell's Non-locality Theorem and by the technological feasibility of building quantum computers and other purely quantum machines, a few physicists are now taking a worm's-eye view at the perplexing quantum/classical border that separates the quantum underworld from the above-ground world of everyday life.

Physicists have usually assumed that, with few exceptions (superconductors, superfluids), quantum effects are confined to the world of the very small, and become imperceptible as more and more atoms are gathered together to make larger objects. Recent work by Adán Cabello in Seville, Spain, sheds new light on this question through his discovery of a new measure of "quantumness" that gets larger as the number of particles increases.

Cabello's Quantum Contexuality in Complex Systems focuses on a generic system consisting of an assembly of a number "n" of elemental two-state quantum systems called "qubits" which might be the basic quantum bits that constitute the heart of some hypothetical quantum computer.

There exist two kinds of measurements that one can make on any complex quantum system--incompatible measurements and compatible measurements. Incompatible measurements (such as position and momentum) are intrinsic features of the quantum world--never found in classical reality. Incompatible measurements (say A and B) obey Heisenberg's Uncertainty Principle--the more you know about quantity A, the less you can know about B. Another curious feature of incompatible measurements is that THEY DO NOT COMMUTE. This means that if you measure A first and then B, you will get a different result then if you do the reverse. In general, as systems get larger, the effects due to non-commuting measurements become quantitatively smaller and incompatible measurements begin to look more and more compatible--in effect becoming indistinguishable from ordinary classical properties.

Cabello focuses his attention on triplets ABC of COMPATIBLE MEASUREMENTS on 3 different qubits. Compatible measurements do not depend on the order of measurement and give the same result if repeated on the same system. Compatible measurements are as close as one can get in the quantum world to a measurement that "looks classical". But Cabello has discovered a quantity "D" which is a simple expression constructed from the results of all possible compatible triplet measurements on a system Z that is a reliable measure of system Z's "deviation from classical behavior." Thus even though each triplet of compatible results by itself may look classical, and perhaps a dozen such measurements may also look classical, Cabello has found a method of looking at all these "classical" measurements taken together that shows that these results cannot possibly be produced by a classical system.

Analogous to Cabello's discovery would be a sophisticated way of looking at all possible outcomes of a poker game and infallibly identifying whether the dealer was cheating (quantum world) or playing fair (classical world) where "n" is the number of players in the game.

The beauty of Cabello's discovery is that his measure "D" of "deviation from classicality" rapidly gets bigger as the number of qubits "n" increases, so his measure D is an example of a quantum effect that persists and is even enhanced as the system gets bigger and bigger. The drawback of Cabello's measure D however is that the number of submeasurements that make up this measure becomes combinatorially large as the size n of the system increases. Thus measuring D for large systems is effectively impractical. On the other hand, Cabello's discovery of a "measure of quantumness" that can be calculated from ostensibly classical results lends hope to the possibility of discovering other such measures that have the same property of increasing with system size but are easier to implement.

In poker game terms, Cabello has discovered how to calculate a "deviation from fairness"--a measure of how much the dealer is cheating--that grows exponentially larger as the number of players increases.

Bravo, Señor Cabello from Seville. Your remarkable discovery moves us one step closer to the quantum tantric goal of being able to enjoy quantum-intimate intercourse with larger and larger chunks of Nature.

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