Weak Value, Quasiprobability and Bohmian Mechanics

Fukuda, Kazuki; Lee, Jaeha; Tsutsui, Izumi

doi:10.1007/s10701-016-0054-3

Cited by 3 publications

(4 citation statements)

References 35 publications

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“…Furthermore, the joint description of detection outcomes from noncommuting observables also requires such negative probabilities to correctly represent the history of sequential measurements [135,136,137,138], also demonstrated in a recent experiment [139]. Moreover, even weak measurements can be characterized via the technique of quasiprobability distributions [140,141].…”

Section: Quasiprobabilities For Other Forms Of Quantumnessmentioning

confidence: 99%

Quasiprobability distributions for quantum-optical coherence and beyond

Sperling

Vogel

2020

Phys. Scr.

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We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique. Regularization and convolution methods are specifically considered as they are accessible in experiments. We further discuss more general quantum systems for which the concept of negative probabilities can be generalized, being highly relevant for quantum information science. For analyzing quantum superpositions, we apply recently developed approaches to visualize quantum coherence of states via negative quasiprobability representations, including regularized quasiprobabilities for light and more general quantum correlated systems.

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Section: Quasiprobabilities For Other Forms Of Quantumnessmentioning

confidence: 99%

Quasiprobability distributions for quantum-optical coherence and beyond

Sperling

Vogel

2020

Phys. Scr.

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“…(21) and (28), for the projection operator A a postselected on measurement result B = b, are sometimes referred to as 'weak probabilities' [10,17,18,57]. However, here we will follow the common practice of identifying the real part of this quantity as a weak probability [26,29,34,36,58,59].…”

Section: A Weak Joint Probabilities and Weak Puritymentioning

confidence: 99%

“…It gives rise to the notion of anomalous weak value for an observable [1,2], recently sharpened in [4]. The concepts of weak measurements and weak values have since been generalized in various directions [5][6][7][8][9][10] and have found numerous applications [11][12][13][14][15][16][17][18][19][20][21][22][23]. However, while the separate real and imaginary components of weak values have been given various interpretations in the literature [21,[24][25][26][27][28][29][30], the weak value itself as a complex number has not.…”

Section: Introductionmentioning

confidence: 99%

Products of weak values: Uncertainty relations, complementarity, and incompatibility

Hall

Pati

2016

Phys. Rev. A

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The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the standard Heisenberg uncertainty relation to be derived from a classical uncertainty relation for complex random variables. We show this formula also leads to strong uncertainty relations for unitary operators, and underlies an interpretation of weak values as optimal (complex) estimates of quantum observables. Furthermore, we show that two incompatible observables that are weakly and strongly measured in a weak measurement context obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values. Moreover, general tradeoff relations, between weak purity, quantum purity and quantum incompatibility, and also between weak and strong joint probability distributions, are obtained based on products of real and imaginary components of weak values, where these relations quantify the degree to which weak probabilities can take anomalous values in a given context.

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“…For example, quasiprobabilities can be generalized to qudits [64], which are particularly relevant in the context of quantum information and communication [65], as well as to study the quantum property of the spin [66][67][68]. Furthermore, finite-dimensional quasiprobabilities relate to so-called weak measurements [69] and enable the efficient estimation of actual measurement-outcome probabilities [70].…”

Section: Introductionmentioning

confidence: 99%

Quasiprobability representation of quantum coherence

Sperling

2018

Phys. Rev. A

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We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement.

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Weak Value, Quasiprobability and Bohmian Mechanics

Cited by 3 publications

References 35 publications

Quasiprobability distributions for quantum-optical coherence and beyond

Quasiprobability distributions for quantum-optical coherence and beyond

Products of weak values: Uncertainty relations, complementarity, and incompatibility

Quasiprobability representation of quantum coherence

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