Wigner function for SU(1,1)

Seyfarth, Ulrich; Klimov, A. B.; Guise, Hubert de; Leuchs, Gerd; Sánchez-Soto, Luis L.

doi:10.22331/q-2020-09-07-317

Cited by 22 publications

(28 citation statements)

References 76 publications

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“…A construction of an

SU (1, 1)

Wigner function has recently been provided in refs. [87, 88]; however, the general

SU (Q, P)

case remains to be solved. Insight into these cases may lead to some interesting results in ideas relating to AdS/CFT in a phase space formalism.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…However the specific case of

SU (1, 1)

has been addressed in a recent paper. [ 87 ] The

SU (1, 1)

representation of certain quantum systems has proven to be useful in simplifying some particular problems in quantum mechanics. In particular Hamiltonians involving squeezing.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…The central result from ref. [87] the generalized displaced parity operator for

SU (1, 1)

is constructed from Equation (125) and the

SU (1, 1)

generalized parity

{false(- 1 false)}^{K_{z}^{M}}

, yielding

{normalΠ}_{1, 1}^{M} false(ζ false) = S_{M} false(ζ false) {(- 1)}^{K_{z}^{M}} S_{M}^{†} false(ζ false)

as the kernel for

SU (1, 1)

.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…Some of the authors from ref. [87] also looked at the equivalence between

SU (2)

and

SO (3)

in phase space. Such analysis could also be used to go between

SU (1, 1)

and

SO (1, 2)

in phase space, or even generalized to

SO (1, 3)

or higher, to consider relativistic quantum mechanics in phase space.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

See 3 more Smart Citations

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Rundle

Everitt

2021

Adv Quantum Tech

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The phase‐space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including methods of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase space is presented. The formulation to generate a generalized phase‐space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the associated Q and P functions. Examples of how these different formulations are used in quantum technologies are provided, with a focus on discrete quantum systems, qubits in particular. Also provided are some results that, to the authors' knowledge, have not been published elsewhere. These results provide insight into the relation between different representations of phase space and how the phase‐space representation is a powerful tool in understanding quantum information and quantum technologies.

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“…A construction of an

SU (1, 1)

Wigner function has recently been provided in refs. [87, 88]; however, the general

SU (Q, P)

case remains to be solved. Insight into these cases may lead to some interesting results in ideas relating to AdS/CFT in a phase space formalism.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…However the specific case of

SU (1, 1)

has been addressed in a recent paper. [ 87 ] The

SU (1, 1)

representation of certain quantum systems has proven to be useful in simplifying some particular problems in quantum mechanics. In particular Hamiltonians involving squeezing.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…The central result from ref. [87] the generalized displaced parity operator for

SU (1, 1)

is constructed from Equation (125) and the

SU (1, 1)

generalized parity

{false(- 1 false)}^{K_{z}^{M}}

, yielding

{normalΠ}_{1, 1}^{M} false(ζ false) = S_{M} false(ζ false) {(- 1)}^{K_{z}^{M}} S_{M}^{†} false(ζ false)

as the kernel for

SU (1, 1)

.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

“…Some of the authors from ref. [87] also looked at the equivalence between

SU (2)

and

SO (3)

in phase space. Such analysis could also be used to go between

SU (1, 1)

and

SO (1, 2)

in phase space, or even generalized to

SO (1, 3)

or higher, to consider relativistic quantum mechanics in phase space.…”

Section: Phase‐space Formulation Of Finite Quantum Systemsmentioning

confidence: 99%

See 2 more Smart Citations

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Rundle

Everitt

2021

Adv Quantum Tech

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show abstract

“…The nonlinear SU(1,1) interferometers can beat the SNL even without using quantum states as inputs [8]. This type of interferometer consists of two nonlinear processes [9] (sometimes one in a truncated version [10,11]), such as four-wave-mixing (FWM) or parametric downconversion (PDC).…”

Section: Introductionmentioning

confidence: 99%

Spectrally multimode integrated SU(1,1) interferometer

Ferreri

Santandrea

Stefszky

et al. 2021

Quantum

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Nonlinear SU(1,1) interferometers are fruitful and promising tools for spectral engineering and precise measurements with phase sensitivity below the classical bound. Such interferometers have been successfully realized in bulk and fiber-based configurations. However, rapidly developing integrated technologies provide higher efficiencies, smaller footprints, and pave the way to quantum-enhanced on-chip interferometry. In this work, we theoretically realised an integrated architecture of the multimode SU(1,1) interferometer which can be applied to various integrated platforms. The presented interferometer includes a polarization converter between two photon sources and utilizes a continuous-wave (CW) pump. Based on the potassium titanyl phosphate (KTP) platform, we show that this configuration results in almost perfect destructive interference at the output and supersensitivity regions below the classical limit. In addition, we discuss the fundamental difference between single-mode and highly multimode SU(1,1) interferometers in the properties of phase sensitivity and its limits. Finally, we explore how to improve the phase sensitivity by filtering the output radiation and using different seeding states in different modes with various detection strategies.

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Non-classical correlations of accelerated observers interacting with a classical stochastic noise beyond the single mode approximation

2023

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This paper investigates the behaviour of the quantum correlations for an accelerated two-qubit system during its interaction with a classical stochastic field, utilizing the Wigner function and concurrence. The non-classical behaviour is indicated by negative values of the Wigner function, while the degree of entanglement is demonstrated by the concurrence. To consider acceleration and interaction with a common or independent environment, we discard the single-mode approximation and utilize the Unruh construction of the quantum field mode in our analysis. Our results suggest that coherence suppression is caused by the acceleration effect, noise strength, and noise frequency. Through an examination of quantum concurrence, this study analyses the level of quantum entanglement that corresponds positively with negative values of the Wigner function. The findings indicate that coherence degradation in the initial system is reduced when observers interact independently with their environments, as opposed to interacting with a common environment. Additionally, the acceleration of both observers has an impact on coherence reduction. During system evolution, the Wigner function displays collapse and reappearance behaviour, while quantum entanglement undergoes local collapse and revival phenomena. Notably, common noise situations exhibit more rapid variation in both the Wigner function and entanglement compared to independent noise configurations.

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Wigner function for SU(1,1)

Cited by 22 publications

References 76 publications

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Spectrally multimode integrated SU(1,1) interferometer

Non-classical correlations of accelerated observers interacting with a classical stochastic noise beyond the single mode approximation

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