Maximal Violation of Bell’s Inequalities for Continuous Variable Systems

Chen, Zeng-Bing; Pan, Jian-Wei; Guang, Hou; Zhang, Yongde

doi:10.1103/physrevlett.88.040406

Cited by 186 publications

(233 citation statements)

References 34 publications

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“…The detailed calculation is given in [9], where in order to compute B 4 we introduced pseudospin operators that behave in the same manner as the usual spin 1/2 operators, but the pseudospin operators can be used for continuous quantum variables [18]. Then, we calculated the expectation value of B 4 in both the Bunch-Davies vacuum Equation (20) and non-Bunch-Davies vacuum Equation (26).…”

Section: Resultsmentioning

confidence: 99%

Bell Inequality and Its Application to Cosmology

Kanno

Soda

2017

Galaxies

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Abstract:One of the cornerstones of inflationary cosmology is that primordial density fluctuations have a quantum mechanical origin. However, most physicists consider that such quantum mechanical effects disappear in CMB data due to decoherence. In this conference report, we show that the violation of Bell inequalities in an initial state of our universe increases exponentially with the number of modes to measure in inflation. This indicates that some evidence that our universe has a quantum mechanical origin may survive in CMB data, even if quantum entanglement decays exponentially afterward due to decoherence.

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Section: Resultsmentioning

confidence: 99%

Bell Inequality and Its Application to Cosmology

Kanno

Soda

2017

Galaxies

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“…From reference [7], the violation of CHSH inequality for the original EPR state can reach the Cirel'son bound 2 √ 2.…”

Section: Introductionmentioning

confidence: 99%

“…In the limit r → ∞, when the original EPR state is recovered, a significant violation of Bell inequality takes place, however, the violation is not very strong. To avoid the unsatisfactory feature, Chen et al [7] introduced "pseudospin" operators based on parity, due to the fact that the degree of quantum nonlocality that we can uncover crucially depends not only on the given quantum state but also on the "Bell operator" [8].…”

Section: Introductionmentioning

confidence: 99%

Multicomponent Bell inequality and its violation for continuous-variable systems

Chen

Kwek

et al. 2005

Phys. Rev. A

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Multi-component correlation functions are developed by utilizing d-outcome measurements. Based on the multi-component correlation functions, we propose a Bell inequality for bipartite d-dimensional systems. Violation of the Bell inequality for continuous variable (CV) systems is investigated. The violation of the original Einstein-Podolsky-Rosen state can exceed the Cirel'son bound, the maximal violation is 2.96981. For finite value of squeezing parameter, violation strength of CV states increases with dimension d. Numerical results show that the violation strength of CV states with finite squeezing parameter is stronger than that of original EPR state.

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“…However, further studies of quantum nonlocality used mainly Bohm's version [4] of the EPR states instead of the original EPR states with continuous degrees of freedom. In recent years, quantum nonlocality for position-momentum variables associated with the original EPR states was analyzed [19][20][21][22][23]. In particular, violations of the Bell-type inequalities by the "regularized" EPR states produced in a pulsed nondegenerate optical parametric amplifier was experimentally observed by using homodyning with weak coherent fields and photon counting [22].…”

mentioning

confidence: 99%

“…In this paper we demonstrate the HES as a valuable resource in quantum information processing, building an interesting link between quantum information protocols of discrete and continuous variables. Quantum nonlocality of the HES is also analyzed by using the recently developed formulation [23]. For usual two-qubit (qubit-1 and qubit-2) systems, one can introduce the following Bell-basis spanned by the two-qubit states Ψ ± 1,2 = 1 √ 2 (|↑ 1 |↓ 2 ± |↓ 1 |↑ 2 ) ,…”

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confidence: 99%

Quantum nonlocality and applications in quantum-information processing of hybrid entangled states

2002

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The hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity system, have exactly one ebit of entanglement, but are not maximally entangled. We demonstrate this by showing that they violate, but in general do not maximally violate, Bell's inequality due to Clauser, Horne, Shimony and Holt. These states are interesting in that they exhibit the entanglement between two distinct degrees of freedom (one is discrete and another is continuous). We then demonstrate these entangled states as a valuable resource in quantum information processing including quantum teleportation, entanglement swapping and quantum computation with "parity qubits". Our work establishes an interesting link between quantum information protocols of discrete and continuous variables. [19][20][21][22][23]. In particular, violations of the Bell-type inequalities by the "regularized" EPR states produced in a pulsed nondegenerate optical parametric amplifier was experimentally observed by using homodyning with weak coherent fields and photon counting [22].In connection with the applicability of quantum superposition principle on a macroscopic scale, Schrödinger [5] described a gedanken experiment, in which a cat is placed in a quantum superposition of being dead and alive while entangled with a single radioactive atom. The mesoscopic equivalents of the Schrödinger-cat states [called hybrid entangled states (HES) in the subsequent discussion] have been experimentally realized for a 9 Be + ion in traps [24] and atoms in high-Q cavities [25]. Particularly, in the trapped ion experiment [24], the HES were generated by entangling ion's internal states (|↑, ↓ in the terminology of spin-1/2 particles) with discrete spectrum and motional states with continuous spectrum:where the motional states |x 1 and |x 2 of the ion are two distinguishable wave packets of a harmonic oscillator and thus denote quantum states with continuous variables. For the atom-cavity system, the entanglement of the type (1) occurs between a microwave cavity field and an atom [25]. These HES are of great theoretical interest in addressing some fundamental issues, such as decoherence and the quantum/classical boundary [24][25][26]. The trapped-ion system is a strong candidate for quantum computation [1,27,28]. In this paper we demonstrate the HES as a valuable resource in quantum information processing, building an interesting link between quantum information protocols of discrete and continuous variables. Quantum nonlocality of the HES is also analyzed by using the recently developed formulation [23]. For usual two-qubit (qubit-1 and qubit-2) systems, one can introduce the following Bell-basis spanned by the two-qubit states Ψ ± 1,2 = 1 √ 2 (|↑ 1 |↓ 2 ± |↓ 1 |↑ 2 ) ,The pairs of qubits are maximally entangled when they are in these states. An analogous Bell-basis spanned by four HES ψ ± 1,2 (z) = 1 √ 2 (|↑ 1 |z o2 ± |↓ 1 |z e2 ) , 1

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Maximal Violation of Bell’s Inequalities for Continuous Variable Systems

Cited by 186 publications

References 34 publications

Bell Inequality and Its Application to Cosmology

Bell Inequality and Its Application to Cosmology

Multicomponent Bell inequality and its violation for continuous-variable systems

Quantum nonlocality and applications in quantum-information processing of hybrid entangled states

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