Strong correspondence principle for joint measurement of conjugate observables

Lorenzo, Antonio Di

doi:10.1103/physreva.83.042104

Cited by 12 publications

(17 citation statements)

References 36 publications

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“…Equations (18) and (19), minus the contribution of the finite readout resolution, were already derived in Ref. [33]. We remark that there is a connection between the noises, due to the Kennard inequality, or better, to the canonically invariant generalization proved by Schrödinger [38] and Robertson [39].…”

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confidence: 83%

“…A rigorous proof, generalizing results presented in Refs. [33,34], that this is the correct formula will be provided elsewhere [35]. If no measurement of X was performed, thenK(−τ + 0) −K(−τ − 0) = 0, so that…”

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confidence: 99%

“…An analogous situation happens with the variablê J K . The correct prescription, which can be proved rigorously [8,33], is to consider…”

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confidence: 99%

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Correlations between Detectors Allow Violation of the Heisenberg Noise-Disturbance Principle for Position and Momentum Measurements

Lorenzo

2013

Phys. Rev. Lett.

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Heisenberg formulated a noise-disturbance principle stating that there is a tradeoff between noise and disturbance when a measurement of position and a measurement of momentum are performed sequentially, and another principle imposing a limitation on the product of the uncertainties in a joint measurement of position and momentum. We prove that the former, the Heisenberg sequential noise-disturbance principle, holds when the detectors are assumed to be initially uncorrelated from each other, but that it can be violated for some properly correlated initial preparations of the detectors.

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confidence: 83%

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confidence: 99%

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Correlations between Detectors Allow Violation of the Heisenberg Noise-Disturbance Principle for Position and Momentum Measurements

Lorenzo

2013

Phys. Rev. Lett.

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“…It can be shown that this measurement is described by the probability distribution [45] W (x, p) = dx dp dγ…”

Section: Simultaneous Measurements Of Position and Momentummentioning

confidence: 99%

Quasi-probability distributions for observables in dynamic systems

Hofer

2017

Quantum

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We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.

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“…In doing so, we propose a generalization of the Moyal function [11]. The justification for this choice is that the Moyal function has revealed itself to be an extremely useful tool for describing the statistics of joint and sequential measurements of momentum and position [12,13].…”

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confidence: 99%

Quantum state tomography from a sequential measurement of two variables in a single setup

Lorenzo

2013

Phys. Rev. A

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We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables,Â andB, the eigenstates of which form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.

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Strong correspondence principle for joint measurement of conjugate observables

Cited by 12 publications

References 36 publications

Correlations between Detectors Allow Violation of the Heisenberg Noise-Disturbance Principle for Position and Momentum Measurements

Correlations between Detectors Allow Violation of the Heisenberg Noise-Disturbance Principle for Position and Momentum Measurements

Quasi-probability distributions for observables in dynamic systems

Quantum state tomography from a sequential measurement of two variables in a single setup

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