Measurements of the probability distribution of the operationally defined quantum phase difference

Noh, Joseph J.; Fougères, Alain-Jérôme; Mandeļ, L.

doi:10.1103/physrevlett.71.2579

Cited by 96 publications

(46 citation statements)

References 31 publications

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“…Another example is in the operational phase measurements of Noh et al [9]. Here certain photo-detector readings are not recorded because they do not lead to meaningful values of the operators being measured.…”

Section: Unbiased Measurementsmentioning

confidence: 99%

Quantum theory of preparation and measurement

Pegg

Barnett

Jeffers

2002

Journal of Modern Optics

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Abstract. The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here we present a more fundamental symmetric postulate from which both predictive and retrodictive probabilities emerge immediately, even where measurement devices more general than those usually considered are involved. We show that the new postulate is perfectly consistent with the conventional postulate.3

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Section: Unbiased Measurementsmentioning

confidence: 99%

Quantum theory of preparation and measurement

Pegg

Barnett

Jeffers

2002

Journal of Modern Optics

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“…6. Even though the probability distributions of the relative phase in the PB and the NFM theory has been argued to be different in the NFM experimental situation [24], some observables can nevertheless apparently lead to the same result. In a similar calculation of the corresponding expression using the SGtheory [1] we replace the cos 2 (φ 2 −φ 1 ) PB operator by the square of the operator…”

Section: The Nfm Operational Approach and Comparison With The Pb Tmentioning

confidence: 99%

On the Quantum Phase Operator for Coherent States

Skagerstam¹,

Bergsjordet²

2004

Phys. Scr.

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In papers by Lynch [Phys. Rev. A41, 2841(1990] and Gerry and Urbanski [Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation laser experiments of Gerhardt, Büchler and Lifkin [Phys. Lett. 49A, 119 (1974)] are in good agreement with the variance of the Pegg-Barnett phase operator for a coherent state, even for a small number of photons. We argue that this is not conclusive. In fact, we show that the variance of the phase in fact depends on the relative phase between the phase of the coherent state and the off-set phase φ0 of the Pegg-Barnett phase operator. This off-set phase is replaced with the phase of a reference beam in an actual experiment and we show that several choices of such a relative phase can be fitted to the experimental data. We also discuss the Noh, Mandel [Phys. Rev. A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase taking post-selection conditions into account.

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“…Adopting the interpretation of Ref. [5], in both these approaches the unnormalized cos and sin functions of the phase shift are detected. However, the normalizations differ in both approaches.…”

Section: Statistical Formulation Of Operational Phase Conceptsmentioning

confidence: 99%

“…Some of them are accenting the theoretical aspects, other the experimental ones. The operational approach formulated by Noh, Fougères and Mandel (NFM) [4,5] is motivated by the correspondence principle in classical wave theory. The interference pattern is adopted for the scheme where the sin and cos function of the phase shift are measured simultaneously in the 8-port homodyne detection.…”

Section: Introductionmentioning

confidence: 99%

Testing of quantum phase in matter-wave optics

et al. 1999

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Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example the discrete Fourier estimation that actually coincides with the operational phase of Noh, Fougères and Mandel is obtained for continuous Gaussian signals with phase modulated mean. Since signals in quantum theory are discrete, a prediction different from that given by the Gaussian hypothesis should be obtained as the best fit assuming a discrete Poissonian statistics of the signal. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of almost any state the optimal phase estimation offers in certain cases a measurable better performance. This has been demonstrated in neutron-optical experiment.

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Measurements of the probability distribution of the operationally defined quantum phase difference

Cited by 96 publications

References 31 publications

Quantum theory of preparation and measurement

Quantum theory of preparation and measurement

On the Quantum Phase Operator for Coherent States

Testing of quantum phase in matter-wave optics

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