Quantum measurement and uncertainty relations in photon polarization

Edamatsu, Keiichi

doi:10.1088/0031-8949/91/7/073001

Cited by 9 publications

(9 citation statements)

References 41 publications

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“…This relation has been experimentally confirmed recently by using a state-preparation method [28][29][30][31][32], weak probe method [33][34][35][36], continuous-variable entangled states [37,38], and others [39,40]. Subsequently, Branciard [41,42], and Ozawa [43] have considered a rigorous relation reads…”

Section: Introductionmentioning

confidence: 82%

Error-disturbance uncertainty relations in Faraday measurements

Ho,

Edamatsu

2021

Preprint

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We examine error-disturbance relations in the quantum measurement of spin systems using an atom-light interface scheme. We model a single spin-1/2 system that interacts with a polarized light meter via a Faraday interaction. We formulate the error and disturbance of the model and examine the uncertainty relations. We found that for the coherent light meter in pure polarization, both the error and disturbance behave the cyclic oscillations due to the Faraday rotation in both the light and spin polarizations. We also examine a class of polarization squeezed light meter, where we apply the phase-space approximation and characterize the role of squeezing. We derive error-disturbance relations for these cases and find that the Heisenberg-Arthurs-Kelly uncertainty is violated while the tight Branciard-Ozawa uncertainty always holds. We note that, in the limit of weak interaction strength, the error and disturbance become to obey the unbiasedness condition and hence the Heisenberg-Arthurs-Kelly relation holds. The work would contribute to our understanding of quantum measurement of spin systems under the atom-light interface framework, and may hold potential applications in quantum metrology, quantum state estimation and control.

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Section: Introductionmentioning

confidence: 82%

Error-disturbance uncertainty relations in Faraday measurements

Ho,

Edamatsu

2021

Preprint

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“…One finds [26] that this turns the (previously weak) measurement scheme preceding the joint measurement into a preparation of the eigenstates of one of the target observables, and one obtains a direct test procedure for measurement noise, and hence for calibration error. Some experimenters (e.g., [32,23]) noticed that the Lund-Wiseman formula for the noise quantities is independent of the strength parameter, and confirmed this experimentally by performing the measurements also in the strong (projective) limit; however, it would be interesting to see whether it is possible to use the data they collected to apply the much simpler, direct method proposed in [26] to determine the errors, namely, by way of an explicit error analysis.…”

Section: Indirect Tests Of Calibration Error Tradeoff Relations Using...mentioning

confidence: 88%

Measurement uncertainty relations: characterising optimal error bounds for qubits

Bullock

Busch

2018

J. Phys. A: Math. Theor.

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In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations.

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“…In particular, it allowed an efficient method for teleportation [21] and was the basis for cryptographic protocols [22][23][24][25].In this work we demonstrate the measurement of nonlocal variables in its original sense, the one which is closest to the standard von Neumann definition of measurement in quantum mechanics [26]. Note, that there exists an alternative scheme [27] alongside a particular proposal for its implementation [28,29], which, however, has the drawback of being a probabilistic measurement, i.e., even with ideal devices it might not provide an outcome.After performing and testing our measurement procedure we apply it to show the peculiar phenomenon of the failure of the product rule for two separate (and thus commuting) local variables which can take place only for pre-and postselected quantum systems [30][31][32]. There have been several demonstrations of the failure of the product rule for weak values, the outcomes of weak measurements [33][34][35] in the context of the Hardy paradox [30].…”

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confidence: 99%

“…In this work we demonstrate the measurement of nonlocal variables in its original sense, the one which is closest to the standard von Neumann definition of measurement in quantum mechanics [26]. Note, that there exists an alternative scheme [27] alongside a particular proposal for its implementation [28,29], which, however, has the drawback of being a probabilistic measurement, i.e., even with ideal devices it might not provide an outcome.…”

mentioning

confidence: 99%

Measurements of Nonlocal Variables and Demonstration of the Failure of the Product Rule for a Pre- and Postselected Pair of Photons

Pan

Wang

et al. 2019

Phys. Rev. Lett.

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We report the first implementation of the von Neumann instantaneous measurements of nonlocal variables which becomes possible due to technological achievements in creating hyperentangled photons. Tests of reliability and of the nondemolition property of the measurements have been performed with high precision showing the suitability of the scheme as a basic ingredient of numerous quantum information protocols. The method allows to demonstrate for the first time with strong measurements a special feature of pre-and postselected quantum systems: the failure of the product rule. It has been verified experimentally that for a particular pre-and postselected pair of particles a single measurement on particle A yields with certainty σ A x = −1, a single measurement on particle B yields with certainty σ B y = −1, and a single nonlocal measurement on particles A and B yields with certainty σ A x σ B y = −1.All known interactions in nature are local. It was thus believed (e.g. [1]) that measurements of nonlocal variables (variables which are related to more than one region of space) are impossible. However, Aharonov and his coauthors [2, 3] showed theoretically that some nonlocal variables can be measured. For two separate locations the sum of local variables, A + B, and the modular sum, (A + B) mod c are always measurable. On the other hand, they also showed that some other nonlocal variables cannot be measured as this would lead to superluminal signalling. Note that if we do not require the measurement to be nondemolition, then theoretically all nonlocal variables are measurable [4], but the procedure has high demands on entanglement resources [5][6][7].Aharonov's main motivation was to shed light on relativistic quantum field theory [2,[8][9][10][11], but the main impact of the analysis of measurements of nonlocal variables was in the field of quantum information [12][13][14][15][16][17][18][19][20]. In particular, it allowed an efficient method for teleportation [21] and was the basis for cryptographic protocols [22][23][24][25].In this work we demonstrate the measurement of nonlocal variables in its original sense, the one which is closest to the standard von Neumann definition of measurement in quantum mechanics [26]. Note, that there exists an alternative scheme [27] alongside a particular proposal for its implementation [28,29], which, however, has the drawback of being a probabilistic measurement, i.e., even with ideal devices it might not provide an outcome.After performing and testing our measurement procedure we apply it to show the peculiar phenomenon of the failure of the product rule for two separate (and thus commuting) local variables which can take place only for pre-and postselected quantum systems [30][31][32]. There have been several demonstrations of the failure of the product rule for weak values, the outcomes of weak measurements [33][34][35] in the context of the Hardy paradox [30]. These, however, are very different results, obtained from many measurements on an ensemble of particles. In our scen...

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Quantum measurement and uncertainty relations in photon polarization

Cited by 9 publications

References 41 publications

Error-disturbance uncertainty relations in Faraday measurements

Error-disturbance uncertainty relations in Faraday measurements

Measurement uncertainty relations: characterising optimal error bounds for qubits

Measurements of Nonlocal Variables and Demonstration of the Failure of the Product Rule for a Pre- and Postselected Pair of Photons

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