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Physical Review A

Experimental test of environment-assisted invariance

L. Vermeyden, Xiongfeng Ma, Jonathan Lavoie, Madeleine Bonsma-Fisher, Urbasi Sinha, Raymond Laflamme, Kevin J. Resch

Published Jan 29, 2015• 13 citations
Publisher

Abstract

Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We benchmark the degree to which nature respects this symmetry by using entangled photon pairs. Our results show quantum states can be $(99.66\ifmmode\pm\else\textpm\fi{}0.04)%$ envariant as measured using the quantum fidelity, and $(99.963\ifmmode\pm\else\textpm\fi{}0.005)%$ as measured using a modified Bhattacharya coefficient, as compared with a perfectly envariant system which would be 100% in either measure. The deviations can be understood by the less-than-maximal entanglement in our photon pairs.

DOI
10.1103/physreva.91.012120

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Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We benchmark the degree to which nature respects this symmetry by using entangled photon pairs. Our results show quantum states can be (99.66\ifmmode±\else\textpm\fi0.04)(99.66\ifmmode\pm\else\textpm\fi{}0.04)%(99.66\ifmmode±\else\textpm\fi0.04) envariant as measured using the quantum fidelity, and (99.963\ifmmode±\else\textpm\fi0.005)(99.963\ifmmode\pm\else\textpm\fi{}0.005)%(99.963\ifmmode±\else\textpm\fi0.005) as measured using a modified Bhattacharya coefficient, as compared with a perfectly envariant system which would be 100% in either measure. The deviations can be understood by the less-than-maximal entanglement in our photon pairs.
Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We benchmark the degree to which nature respects this symmetry by using entangled photon pairs. Our results show quantum states can be 99.66(4)% envariant as measured using the quantum fidelity, and 99.963(5)% as measured using a modified Bhattacharya Coefficient, as compared with a perfectly envariant system which would be 100% in either measure. The deviations can be understood by the less-than-maximal entanglement in our photon pairs.
I show how probabilities arise in quantum physics by exploring the implications of environment-assisted invariance or envariance, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like'' states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Born's rule ${p}_{k}\ensuremath{\propto}{\ensuremath{\mid}{\ensuremath{\psi}}_{k}\ensuremath{\mid}}^{2}$ for the outcomes associated with Schmidt states. The probabilities derived in this manner are an objective reflection of the underlying state of the system---they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge'' of the observer. This envariance-based approach is compared with and found to be superior to prequantum definitions of probability including the standard definition based on the ``principle of indifference'' due to Laplace and the relative frequency approach advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Born's rule: Envariance is enough to establish the dynamical independence of preferred branches of the evolving state vector of the composite system and, thus, to arrive at the environment-induced superselection (einselection) of pointer states, which was usually derived by an appeal to decoherence. The envariant origin of Born's rule for probabilities sheds light on the relation between ignorance (and, hence, information) and the nature of quantum states.
In this thesis, we experimentally test fundamental properties of quantum mechanics, namely \nnon-locality (in the form of three new families of Bell's inequalities) and the symmetry of \nenvariance. To accomplish these we use a Sagnac source of polarization entangled photon \npairs. \nIn chapters one and two we discuss the relevant background information in quantum \ninformation theory, nonlinear optics, experimental realization of polarization entangled \nphotons and a trouble-shooting and maintenance guide for a Saganc source. \nIn chapter three we experiment with a set of three newly derived families of Bell's \ninequalities. These three families are predicted to yield the largest volume of violation of \nthe local hidden variable models (LHVM). Our experimental results are in good agreement \nwith those predictions and therefore, represent the largest volume of experimental violation \nof LHVM to date. We showed a violation of up to 30 sigma from what is predicted by LHVM, \nand our results followed closely to the predictions of quantum mechanics. \nIn chapter four we experimentally test envariance, an assisted-symmetry exhibited by \nspecifi c quantum systems. Envariance is a fundamental property in the quantum world that \nhas lacked, until now, extensive experimental study. The symmetry has ramifi cations in the \nfoundations of quantum mechanics, and plays an integral role in a proof of Born's rule [1]. \nOur results serve as a benchmark the property of envariance. We show that experimental \nquantum states can be (99.66+/- 0.04)% envariant over a wide range of transformations, as \nmeasured using the average quantum fi delity [2], and (99.963 +/- 0.005)% as measured using \na modifi ed average Bhattacharya Coeffi cient [3], a measure of the overlap of two probability \ndistributions.
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying the quantum foundational bedrock. A major family of derivations is based on envariance, a recently discovered symmetry of entangled quantum states. Here, we identify and experimentally test three premises central to these envariance-based derivations, thus demonstrating, in the microworld, the symmetries from which the Born rule is derived. Further, we demonstrate envariance in a purely local quantum system, showing its independence from relativistic causality.
Quantum entanglement is among the most fundamental, yet from classical intuition also most surprising properties of the fully quantum nature of physical reality. We report several experiments performed on IBM's Quantum Experience demonstrating envariance - entanglement assisted invariance. Envariance is a recently discovered symmetry of composite quantum systems, which is at the foundational origin of physics and a quantum phenomenon of pure states. These very easily reproducible and freely accessible experiments on Quantum Experience provide simple tools to study the properties of envariance, and we illustrate this for several cases with "quantum universes" consisting of up to five qubits.