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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Experimental test of error-disturbance relations in generalized photon-polarization measurements

So-Young Baek, Fumihiro Kaneda, Masanao Ozawa, Keiichi Edamatsu

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We report an experimental test of Ozawa’s relation for a single-photon polarization qubit, exploiting an indirect measurement model that breaks Heisenberg’s relation throughout the range of our experimental parameter and yet validates Ozawa’s relation.
DOI
10.1364/qim.2013.w6.12

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The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.
Abstract Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an experimental test of the error-disturbance uncertainty relations in photon polarization measurements. Using a generalized, strength-variable measurement of a single photon polarization state, we experimentally evaluate the error and disturbance in the measurement process and demonstrate the validity of recently proposed uncertainty relations.
The original Heisenberg error-disturbance relation was recently shown to be not universally valid and two different approaches to reformulate it were proposed. The first one focuses on how the error and disturbance of two observables AAA and BBB depend on a particular quantum state. The second one asks how a joint measurement of AAA and BBB affects their eigenstates. Previous experiments focused on the first approach. Here we focus on the second one. First, we propose and implement an extendible method of quantum-walk-based joint measurements of noisy Pauli operators to test the error-disturbance relation for qubits introduced in the work of Busch et al. [Phys. Rev. A 89, 012129 (2014)], where the polarization of the single photon, corresponding to a walker's auxiliary degree of freedom that is commonly known as a coin, undergoes a position- and time-dependent evolution. Then we formulate and experimentally test a universally valid state-dependent relation for three mutually unbiased observables. We therefore establish a method of testing error-disturbance relations.