Sharpening Occam's Razor with Quantum Mechanics

Mile Gu, Karoline Wiesner, Elisabeth Rieper, Vlatko Vedral

(Submitted on 9 Feb 2011 (v1), last revised 9 Aug 2011 (this version, v4))

Mathematical models, algorithms that encapsulate the behaviour of systems of interest, underpin the heart of quantitative science. They output the future behaviour of the system, when fed knowledge of its initial conditions. In the spirit of Occam's razor, simpler is better; should two models equally simulate the future, the one that requires less initial data is preferred. For almost all stochastic processes, even the provably simplest classical models have room for improvement. For each bit of predictive output, they generically require more than a single bit of input. We show that by encoding possible initial conditions into non-orthogonal quantum states, we can systematically construct predictive models that break this classical bound. This indicates that the device of minimal entropy that exhibits such statistics must necessarily feature quantum dynamics, and that certain phenomena could be significantly simpler than classically possible, should quantum effects be involved.

Comments: 6 pages, 3 figures

Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

Cite as: arXiv:1102.1994v4 [quant-ph]

Mile Gu, Karoline Wiesner, Elisabeth Rieper, Vlatko Vedral

(Submitted on 9 Feb 2011 (v1), last revised 9 Aug 2011 (this version, v4))

Mathematical models, algorithms that encapsulate the behaviour of systems of interest, underpin the heart of quantitative science. They output the future behaviour of the system, when fed knowledge of its initial conditions. In the spirit of Occam's razor, simpler is better; should two models equally simulate the future, the one that requires less initial data is preferred. For almost all stochastic processes, even the provably simplest classical models have room for improvement. For each bit of predictive output, they generically require more than a single bit of input. We show that by encoding possible initial conditions into non-orthogonal quantum states, we can systematically construct predictive models that break this classical bound. This indicates that the device of minimal entropy that exhibits such statistics must necessarily feature quantum dynamics, and that certain phenomena could be significantly simpler than classically possible, should quantum effects be involved.

Comments: 6 pages, 3 figures

Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

Cite as: arXiv:1102.1994v4 [quant-ph]

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