Different operational meanings of continuous variable Gaussian entanglement criteria and Bell inequalities

Buono, Daniela; Nocerino, Gaetano; Solimeno, S.; Porzio, Alberto

doi:10.1088/1054-660x/24/7/074008

Cited by 11 publications

(12 citation statements)

References 33 publications

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“…Thus, there exists a relation between en-tanglement and EPR correlations. However, there are Gaussian states that are entangled, but are compatible with a local hidden variable theory, and there are entangled Gaussian states that are non-local [5,6]. This confirms the existence of different types of quantum correlations and non-locality.…”

Section: Introductionsupporting

confidence: 55%

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Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

et al. 2016

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One examines putative corrections to the Bell operator due to the noncommutativity in the phasespace. Starting from a Gaussian squeezed envelop whose time evolution is driven by commutative (standard quantum mechanics) and noncommutative dynamics respectively, one concludes that, although the time evolving covariance matrix in the noncommutative case is different from the standard case, the squeezing parameter dominates and there are no noticeable noncommutative corrections to the Bell operator. This indicates that, at least for squeezed states, the privileged states to test Bell correlations, noncommutativity versions of quantum mechnics remains as nonlocal as quantum mechanics itself.

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Section: Introductionsupporting

confidence: 55%

“…Thus, one has a Bell operator, B(I, n, t 1 ), that depends on a free parameter I, and on the state properties n and t 1 . Looking for the maximum violation for a given state, one should maximize the Bell operator in terms of the free parameter I [5],…”

Section: Nc Two Mode Squeezed Statementioning

confidence: 99%

Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

et al. 2016

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“…This is proven by applying the Peres-Horodecki-Simon (PHS) [10][11][12] and the Duan Criteria [13]. Both inseparability criteria translate into inequalities written in terms of the CM's elements ( [14], [Equations (8) and 9]).…”

Section: Resultsmentioning

confidence: 99%

Continuous Variable Entanglement in Non-Zero Orbital Angular Momentum States

Pecoraro¹,

Cardano

Marrucci

et al. 2019

11th Italian Quantum Information Science Conference (IQIS2018)

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Orbital angular momentum is a discrete degree of freedom that can access an infinite dimensional Hilbert space, thus enhancing the information capacity of a single optical beam. Continuous variables field quadratures allow achieving some quantum tasks in a more advantageous way with respect to the use of photon-number states. Here, we use a hybrid approach realizing bipartite continuous-variable Gaussian entangled state made up of two electromagnetic modes carrying orbital angular momentum. A q-plate is used for endowing a pair of entangled beams with such a degree of freedom. This quantum state is then completely characterized thanks to a novel design of a homodyne detector in which also the local oscillator is an orbital angular momentum-carrying beams so allowing the direct detection of vortex modes quadratures.

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“…Once expressed in terms of continuous variable systems, the original formulation of the procedure brings about the nonlocal properties shared by two subsystems in the EPR state with perfect correlations in both position and momentum coordinates. These correlations can be expressed in the language of bipartite Gaussian states [37] for which the corresponding EPR phase-space Wigner function is written as [25]:…”

Section: Teleportation Fidelity In the Nc Phase-spacementioning

confidence: 99%

Quantum cloning and teleportation fidelity in the noncommutative phase-space

Leal¹,

Bernardini²,

Bertolami³

2019

J. Phys. A: Math. Theor.

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The formulation of the no-cloning theorem in the framework of phase-space noncommutative (NC) quantum mechanics (QM) is examined, and its implications for the computation of quantum cloning probabilities and teleportation fidelity are investigated through the Weyl-Wigner formulation of QM. The principles of QM re-edited in terms of a deformed Heisenberg-Weyl algebra are shown to provide a covariant formulation for the quantum fidelity, through which the results from the no-cloning theorem for the ordinary QM can be reproduced. Besides exhibiting an explicit correspondence between standard and NC QM for Gaussian Wigner functions, our results suggest a feasible interpretation for the NC continuous variable quantum cloning given in terms of quantum teleportation protocols.

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Different operational meanings of continuous variable Gaussian entanglement criteria and Bell inequalities

Cited by 11 publications

References 33 publications

Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

Bell operator and Gaussian squeezed states in noncommutative quantum mechanics

Continuous Variable Entanglement in Non-Zero Orbital Angular Momentum States

Quantum cloning and teleportation fidelity in the noncommutative phase-space

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