Proposal for a Loophole-Free Bell Test Using Homodyne Detection

García−Patrón, Raúl; Fiurášek, Jaromı́r; Cerf, Nicolas J.; Wenger, Jérôme; Tualle-Brouri, Rosa; Grangier, P.

doi:10.1103/physrevlett.93.130409

Cited by 277 publications

(166 citation statements)

References 38 publications

(36 reference statements)

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“…As for example, it is known that nG is crucial for the realization of entanglement distillation [9][10][11], quantum error correction [12] and cluster states quantum computation [13,14]. Besides, a non-Gaussian measurement and/or non-Gaussian states are crucial to observe violation of loophole free Bell tests with continuous variables [15][16][17][18][19][20][21][22][23][24]. In addition, improvement of quantum teleportation and quantum cloning of coherent states can be obtained by using respectively non-Gaussian states or non-Gaussian operations [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Quantifying non-Gaussianity for quantum information

2010

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We address the quantification of non-Gaussianity of states and operations in continuous-variable systems and its use in quantum information. We start by illustrating in details the properties and the relationships of two recently proposed measures of non-Gaussianity based on the Hilbert-Schmidt (HS) distance and the quantum relative entropy (QRE) between the state under examination and a reference Gaussian state. We then evaluate the non-Gaussianities of several families of non-Gaussian quantum states and show that the two measures have the same basic properties and also share the same qualitative behaviour on most of the examples taken into account. However, we also show that they introduce a different relation of order, i.e. they are not strictly monotone each other. We exploit the non-Gaussianity measures for states in order to introduce a measure of non-Gaussianity for quantum operations, to assess Gaussification and de-Gaussification protocols, and to investigate in details the role played by non-Gaussianity in entanglement distillation protocols. Besides, we exploit the QRE-based non-Gaussianity measure to provide new insight on the extremality of Gaussian states for some entropic quantities such as conditional entropy, mutual information and the Holevo bound. We also deal with parameter estimation and present a theorem connecting the QRE non-Gaussianity to the quantum Fisher information. Finally, since evaluation of the QRE non-Gaussianity measure requires the knowledge of the full density matrix, we derive some experimentally friendly lower bounds to non-Gaussianity for some class of states and by considering the possibility to perform on the states only certain efficient or inefficient measurements.

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Section: Introductionmentioning

confidence: 99%

Quantifying non-Gaussianity for quantum information

2010

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“…Other coherent superposition operations, such as tâ+rb † and tââ † +râ †â , were also proposed to produce an arbitrary photon-number entangled state in a finite dimension, N n=0 c n |n, n AB [42]. Due to the fact that entanglement characteristics of Gaussian states are enhanced by a non-Gaussian operation [9][10][11][12][13][14][15][16][17][18][19][20][21], it is natural to have a question about whether entanglement characteristics of non-Gaussian states are enhanced by a non-Gaussian operation. In particular, we are interested in non-Gaussian states which do not have any two-mode squeezing properties in order to determine their own usefulness compared with a typical Gaussian entangled state.…”

Section: Introductionmentioning

confidence: 99%

“…Some of us have recently proposed entanglement criteria beyond the Gaussian regime, where the entanglement criteria including all orders of EPR correlations can be measured with homodyne detection [8]. Non-Gaussian entangled states provide the benefits on enhancing violation of Bell's inequality [9][10][11], and degree of entanglement [12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

Lee

2013

Phys. Rev. A

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We investigate how the entanglement characteristics of a non-Gaussian entangled state are increased or decreased by a local photon subtraction operation. The non-Gaussian entangled state is generated by injecting a single-mode non-Gaussian state and a vacuum state into a 50:50 beam splitter. We consider a photon-added coherent stateâ † |α and an odd coherent state |α − | − α as a single-mode non-Gaussian state. In the regime of small |α|, we show that the performance of quantum teleportation and the second-order Einstein-Podolsky-Rosen-type correlation can both be enhanced, whereas the degree of entanglement decreases, for the output state when a local photon subtraction operation is applied to the non-Gaussian entangled state. The counterintuitive effect is more prominent in the limit of |α| ∼ 0.

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“…The progress of these experiments promises the realizations of more complicated applications of photon subtraction proposed so far, including the improvement of quantum teleportation [7,8,9] and entanglement-assisted coding [10], entanglement distillation [11], loophole free tests of Bell's inequalities [12,13,14], and optical quantum computations in quadrature basis [15,16] or superposed coherent state basis [17,18]. In the last application, |C ± (α) with appropriate α is required as an ancillary state.…”

Section: Introductionmentioning

confidence: 99%

Conditional generation of an arbitrary superposition of coherent states

Takeoka

Sasaki

2007

Phys. Rev. A

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We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.

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Proposal for a Loophole-Free Bell Test Using Homodyne Detection

Cited by 277 publications

References 38 publications

Quantifying non-Gaussianity for quantum information

Quantifying non-Gaussianity for quantum information

Increasing and decreasing entanglement characteristics for continuous variables by a local photon subtraction

Conditional generation of an arbitrary superposition of coherent states

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