Quantum networks for concentrating entanglement

Kaye, Phillip; Mosca, Michele

doi:10.1088/0305-4470/34/35/319

Cited by 18 publications

(14 citation statements)

References 4 publications

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“…The Schmidt projection method requires at least two nonmaximally entangled pairs and becomes efficient for large numbers of pairs. It is based on a collective measurement (of the "Hamming weight" [127]) of all qubits at one side projecting all pairs onto a subspace spanned by states having a common Schmidt coefficient. The measurement result is then classically communicated to the other side (alternatively, the same collective measurement performed at the other side would yield the same result and make classical communication dispensable).…”

Section: Entanglement Distillationmentioning

confidence: 99%

Quantum Communication with Continuous Variables

Loock

2002

Fortschr. Phys.

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Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous‐variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous‐variable entanglement and show how to make it. The members of a family of multi‐mode states are found to be truly multi‐party entangled with respect to all their modes. These states also violate multi‐party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi‐party continuous‐variable entanglement. Various quantum communication protocols based on the continuous‐variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous‐variable entanglement swapping. We highlight the similarities and differences between continuous‐variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi‐party generalization of quantum teleportation. This so‐called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no‐cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase‐insensitive amplifier and beam splitters.

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Section: Entanglement Distillationmentioning

confidence: 99%

Quantum Communication with Continuous Variables

Loock

2002

Fortschr. Phys.

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“…Hayden and Winter (2003) characterized the classical communication cost of entanglement dilution, as did Harrow and Lo (2004). Kaye and Mosca (2001) developed practical networks for entanglement concentration, and recently, Blume-Kohout et al (2014) took this line of research a step further by considering streaming protocols for entanglement concentration. Hayashi and Matsumoto (2001) also developed protocols for universal entanglement concentration.…”

Section: History and Further Readingmentioning

confidence: 99%

Preface to the Second Edition

Wilde¹

2016

Quantum Information Theory

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“…. x k−1 ) for k = n. The Hamming weight can be efficiently computed as shown in [KM01]. Then we simply need to reversibly compute the ω k satisfying cos 2 (2πω k ) = αx 1 x 2 ...x k−1 0 αx 1 x 2 ...x k−1 2 + poly(ǫ).…”

Section: Efficiency: An Examplementioning

confidence: 99%