Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels

Deutsch, David; Ekert, Artur; Jozsa, Richard; Macchiavello, Chiara; Popescu, Sandu; Sanpera, Anna

doi:10.1103/physrevlett.77.2818

Cited by 1,131 publications

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“…Entanglement distillation 4,5 extracts from several shared copies of weakly entangled mixed states a single copy of a highly entangled state using only local quantum operations and classical communication between the two parties sharing the states. This turned out to be a very challenging task for continuous-variable states, because it was proved that it is impossible to distil Gaussian entangled states by means of the experimentally accessible Gaussian operations 18,19 .…”

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Preparation of distilled and purified continuous-variable entangled states

et al. 2008

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The distribution of entangled states of light over long distances is a major challenge in the field of quantum information. Optical losses, phase diffusion and mixing with thermal states lead to decoherence and destroy the non-classical states after some finite transmission-line length. Quantum repeater protocols 1,2 , which combine quantum memory 3 , entanglement distillation 4,5 and entanglement swapping 6 , were proposed to overcome this problem. Here we report on the experimental demonstration of entanglement distillation in the continuous-variable regime 7-9 . Entangled states were first disturbed by random phase fluctuations and then distilled and purified using interference on beam splitters and homodyne detection. Measurements of covariance matrices clearly indicate a regained strength of entanglement and purity of the distilled states. In contrast to previous demonstrations of entanglement distillation in the complementary discrete-variable regime 10,11 , our scheme achieved the actual preparation of the distilled states, which might therefore be used to improve the quality of downstream applications such as quantum teleportation 12 .Quantum information makes use of the special properties of quantum states to improve the quality of communication and information processing tasks. Generally, a quantized field can be described by the number operator or alternatively by two non-commuting position and momentum-like operators. The corresponding measurement results have either discrete or continuous spectra and form the basis of discrete-variable or continuous-variable quantum information, respectively. In the regime of continuous variables, entangled states of light can be deterministically generated in optical parametric amplifiers (OPAs), precisely manipulated with linear optics and measured with very high efficiency in balanced homodyne detectors. These entangled two-mode squeezed states show Gaussian probability distributions and were used for quantum teleportation 12 and entanglement swapping 13,14 . Entangled states of the collective spins of two atomic ensembles analogous to two-mode squeezed states have been generated 15 , storage of quantum states of light in an atomic memory has been demonstrated 3 and teleportation from light onto an atomic ensemble has been reported 16 . High-speed quantum cryptography with coherent light beams and homodyne detection has been demonstrated 17 . All these spectacular achievements reveal the great potential of this approach to quantum information processing.A missing piece in this toolbox has been a feasible protocol for entanglement distillation and purification. Entanglement distillation 4,5 extracts from several shared copies of weakly entangled mixed states a single copy of a highly entangled state using only local quantum operations and classical communication between the two parties sharing the states. This turned out to be a very challenging task for continuous-variable states, because it was proved that it is impossible to distil Gaussian entangled states by ...

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Preparation of distilled and purified continuous-variable entangled states

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“…Popescu's construction [14] did not work for spaces with fewer than 5 2 dimensions, but similar protocols have been found [16][17][18][19] for Werner pairs of spin-1 2 particles. If each one of these pairs is tested separately, the CHSH inequality is satisfied, as we know.…”

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confidence: 89%

“…[16][17][18][19] for advance copies of their articles, and to N. D. Mermin and S. Popescu for an illuminating exchange of correspondence. This work was supported by the Gerard Swope Fund, and the Fund for Encouragement of Research.…”

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Bell Inequalities with Postselection

Peres

1997

Potentiality, Entanglement and Passion-at-a-Distance

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Experimental tests of Bell inequalities ought to take into account all detection events. If the latter are postselected, and only some of these events are included in the statistical analysis, a Bell inequality may be violated, even by purely classical correlations. The paradoxical properties of Werner states, recently pointed out by Popescu, can be explained as the result of a postselection of the detection events, or, equivalently, as due to the preparation of a new state by means of a nonlocal process.

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“…This approach combines both the potential for relatively long relaxation times and large degree of design flexibility, and probably represents one of the best, if not the best, hope for realization of a quantum computer of medium complexity. Such a computer, while not being sufficient for factorization of large numbers of practical interest, could be sufficiently complex to perform privacy amplification [12,13] in quantum communication channels.…”

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Adiabatic quantum computation with Cooper pairs

Averin

1998

Solid State Communications

288

256

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We propose a new variant of the controlled-NOT quantum logic gate based on adiabatic level-crossing dynamics of the q-bits. The gate has a natural imple- Practical realization of a quantum computer requires, however, very precise and reversible time evolution of complex quantum mechanical systems, the fact that gives rise to serious doubts [4] as to whether even the simplest version of a quantum computer will ever become a reality. It is therefore important to look into various possible ways of implementing simple elements of quantum computer -quantum logic gates in order to find the optimal approach to building such a computer. Generally speaking, a quantum gate should satisfy two contradictory requirements: being isolated from the outside world in order to maintain 1

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Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels

Cited by 1,131 publications

References 14 publications

Preparation of distilled and purified continuous-variable entangled states

Preparation of distilled and purified continuous-variable entangled states

Bell Inequalities with Postselection

Adiabatic quantum computation with Cooper pairs

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