Monday, February 24, 2014

Who's on First!?

“On the Uncertainty of the Ordering of Nonlocal Wavefunction Collapse when Relativity is Considered,”

by Chris D. Richardson and Jonathan P. Dowling

This preprint on the ArXiv by my former PhD student, Chris Richardson, and me, is not getting enough of the well-deserved publicity that it warrants so here I am to shamelessly promote it. (That and Chris will shortly be looking for a job.) This is really 90% Chris’s work with 10% motivational pep talks from me to him. In a previous blog post, “On the Curious Consistency of Non-Relativistic Quantum Theory with Non-Quantum Relativity Theory,” I blathered on about how odd it was that non-relativistic quantum theory always seemed to be consistent with ordinary relativity theory; even though we have no right to expect that these two theories should be consistent and every right to believe they should flat out contradict each other. This curiousness Nicolas Gisin calls the “tension” between the two theories and Gisin has even done an experiment of the EPR type with a well separated Alice and Bob, but with Bob placed in a moving reference frame (compared to Alice) to try to measure the ‘speed of collapse’ of the two-particle wave function. Gisin and his group conclude that the speed of collapse is some 10,000 times faster than the speed of light (which is consistent with infinitely fast).

This experiment motivated Chris and I to think about a closely related problem; a problem that in fact motivated Gisin’s experiment in the first place. In non-relativistic quantum theory, in an EPR experiment, if Alice makes a measurement on her particle then the state of Bob’s particle is supposed to collapse ‘instantaneously and simultaneously’ to the result anti-correlated to Alice’s measurement (if they share, say, a spin-singlet state). But words like ‘instantaneous’ and — Heaven forbid! — ‘simultaneous’ are heresy in non-quantum relativity theory.

This thought experiment gives rise to a purported paradox. If in one reference frame Alice measures first and collapses Bob’s state there can always be an observer in a different inertial frame who thinks Bob measured first and collapsed Alice’s state. The paradox then may be stated, “Who really collapsed whom first?” This curious swapping of temporal order is the paradox.

Now if I was David Deutsch I would tell you to avoid all this collapse nonsense and to instead embrace the Many Worlds Interpretation of Quantum Mechanics but instead Chris and I decided to push this paradox into a small logical corner where we could beat the heck out of it with a purely Copenhagen Gedanken experimental analysis.

The conclusion of our short paper, now in referee limbo in some journal I’d rather not mention (so as to avoid the once and future lawsuits) is that Naturenot the journal! — deploys a type of quantum-mechanical cloaking device upon the experiment to keep the paradox from arising in the first place.

The paroxysm of paradoxism is swept squarely under a round rug.

The crux of our argument is that Alice and Bob’s measurements cannot be made with infinite precision but are constrained by the Heisenberg uncertainty principle — particularly the notorious energy-time uncertainty principle. Since energy and time are not relativistically invariant quantities, different observers in different reference frames must transform their uncertainty principles accordingly.

Therein lies the rug.

To quote the conclusion of our paper; “The uncertainty in time always outruns the time difference induced by the change in reference frames. Neither Alice nor Bob will ever, with certainty, observe the two measurements swap temporal order.”

Paradox, schmäradox!

The curious consistency of quantum theory and relativity theory hides again….

Monday, February 17, 2014

Boson sampling with photon-added coherent states

Kaushik P. Seshadreesan, Jonathan P. Olson, Keith R. Motes, Peter P. Rohde, Jonathan P. Dowling
Boson sampling is a simple and experimentally viable model for non-universal linear optics quantum computing. Boson sampling has been shown to implement a classically hard algorithm when fed with single photons. This raises the question as to whether there are other quantum states of light that implement similarly computationally complex problems. We consider a class of continuous variable states---photon added coherent states---and demonstrate their computational complexity when evolved using linear optical networks and measured using photodetection. We find that, provided the coherent state amplitudes are upper bounded by an inverse polynomial in the size of the system, the sampling problem remains computationally hard.

See: arXiv:1402.0531