Pegg-Barnett phase operators of infinite rank

Vaccaro, John A.; Bonner, R.

doi:10.1016/0375-9601(95)00053-6

Cited by 14 publications

(2 citation statements)

References 20 publications

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“…In any case, however, there will be an inevitable coordinate singularity at some point of the circle where the respective angle variable jumps between the endpoints of the interval. This implies that a momentum observable for an infinite lattice or an angle observable for a bead on a wire can be defined as a multiplicative operator in the corresponding representation but will carry a signature of the parametrization chosen [11,12].…”

Section: Infinite One-dimensional Lattice / Bead On a Wirementioning

confidence: 99%

On the exponential form of the displacement operator for different systems

Potoček

Barnett

2015

Phys. Scr.

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The family of displacement operators D x p ( , ), a central concept in the theory of coherent states of a quantum mechanical harmonic oscillator, has been successfully generalized to systems of quantized, cyclic or finite position coordinates. However, out of the plethora of mutually equivalent expressions for the displacement operators valid in the continuous case, only few are directly applicable in the other systems of interest. The aim of this paper is to strengthen the analogy between the different cases by identifying the root cause of the issues accompanying the straightforward generalization of certain important expressions and, more importantly, offering alternative ones of general validity. Ultimately we arrive at an algorithm allowing one to express any displacement operator as an exponential of a pure imaginary multiple of a generalized 'quadrature' observable that is not obtained by a linear combination of position and momentum observables but rather by a shear transform of one of them in the systemʼs phase space.

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Section: Infinite One-dimensional Lattice / Bead On a Wirementioning

confidence: 99%

On the exponential form of the displacement operator for different systems

Potoček

Barnett

2015

Phys. Scr.

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“…△R • △Q ≥ 1 2 | [R, Q] |, for two incompatible observables R and Q. Another is the entropic uncertainty relation [2,3,4] which quantifies the quantum fluctuations of two observables in terms of entropy. Suppose p(x) is a probability distributions of the measurement outcome x for a random variable X, the Shannon entropy H(X) = − k p k (x)log 2 p k (x) indicates the uncertainty of X.…”

Section: Introductionmentioning

confidence: 99%

The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments

Zou¹,

Mao-Fa²,

Yang³

et al. 2014

Phys. Scr.

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The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments are studied by the time-convolutionless master-equation approach. The influence of non-Markovian effect and detuning on the lower bound of the quantum entropic uncertainty relation and entanglement witness is discussed in detail. The results show that, only if the two non-Markovian reservoirs are identical, increasing detuning and non-Markovian effect can reduce the lower bound of the entropic uncertainty relation, lengthen the time region during which the entanglement can be witnessed, and effectively protect the entanglement region witnessed by the lower bound of the entropic uncertainty relation. The results can be applied in quantum measurement, quantum cryptography task and quantum information processing.

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Controlling Entropic Uncertainty and Quantum Correlation of a Bath of Spins

2021

Int J Theor Phys

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Pegg-Barnett phase operators of infinite rank

Cited by 14 publications

References 20 publications

On the exponential form of the displacement operator for different systems

On the exponential form of the displacement operator for different systems

The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments

Controlling Entropic Uncertainty and Quantum Correlation of a Bath of Spins

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