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arXiv:quant-ph/0605143 · Physical Review A

Procrustean entanglement concentration of continuous-variable states of light

David Menzies, Natalia Korolkova

Published Oct 16, 2006• 15 citations
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Abstract

We propose a Procrustean entanglement concentration scheme for continuous-variable states inspired by the scheme proposed in J. Fiur\`a\ifmmode \check{s}\else \v{s}\fi{}ek et al. [Phys. Rev. A 67, 022304 (2003)]. We show that the eight-port homodyne measurement of J. Fiur\`a\ifmmode \check{s}\else \v{s}\fi{}ek et al. [Phys. Rev. A 67, 022304 (2003)] can be replaced by a balanced homodyne measurement with the advantage of providing a success criterion that allows Alice and Bob to determine if entanglement concentration was achieved. In addition, it facilitates a straightforward experimental implementation.

DOI
10.1103/physreva.74.042315

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We propose a Procrustean entanglement concentration scheme for continuous-variable states inspired by the scheme proposed in J. Fiur`a\ifmmode \check{s}\else \v{s}\fi{}ek et al. [Phys. Rev. A 67, 022304 (2003)]. We show that the eight-port homodyne measurement of J. Fiur`a\ifmmode \check{s}\else \v{s}\fi{}ek et al. [Phys. Rev. A 67, 022304 (2003)] can be replaced by a balanced homodyne measurement with the advantage of providing a success criterion that allows Alice and Bob to determine if entanglement concentration was achieved. In addition, it facilitates a straightforward experimental implementation.
We devise and examine two procrustean entanglement concentration schemes using Quantum Non- Demolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox to the use of a much more general, versatile and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian post-measurement, the second a non-Gaussian ancillary mode and a Gaussian post-measurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function based method in a numerically efficient manner. We then quantify the entanglement increase calculating the Logarithmic Negativity of the output state and discuss and compare the performance of the protocols.
In this thesis, we are concerned with continuous-variable quantum optical state \nengineering protocols. Such protocols are designed to repair or enhance the nonclassical features of a given state. In particular, we build a weak measurement model \nof Gaussian entanglement concentration of the two mode squeezed vacuum state. \nThis model allows the simultaneous description of all possible ancilla system variations. In addition, it provides an explanation of the Gaussian-preserving property of these protocols while providing a success criterion which links all of the degrees of freedom on the ancilla. Following this, we demonstrate the wider application \nof weak measurements to quantum optical state engineering by showing that they allow probabilistic noiseless amplifi cation of photon number. We then establish a connection between weak measurements and entanglement concentration as a fundamental \nresult of weak measurements on entangled probes. After this, we explore the trade-off between Gaussian and non-Gaussian operations in the preparation of non-Gaussian pure states. In particular, we suggest that an operational cost for an arbitrary non-Gaussian pure state is the largest Fock state required for its approximate preparation. We consider the extent to which this non-Gaussian operational cost can be reduced by applying unitary Gaussian operations. This method relies on the identification of a minimal core state for any target non-Gaussian pure state.
We devise and examine two procrustean entanglement concentration schemes using quantum nondemolition (QND) interaction Hamiltonians in the continuous variable regime, applicable for light, for atomic ensembles or in a hybrid setting. We thus expand the standard entanglement distillation toolbox for use of a much more general, versatile, and experimentally feasible interaction class. The first protocol uses Gaussian ancillary modes and a non-Gaussian postmeasurement, the second a non-Gaussian ancillary mode and a Gaussian postmeasurement. We explicitly calculate the density matrix elements of the non-Gaussian mixed states resulting from these protocols using an elegant Wigner-function-based method in a numerically efficient manner. We then quantify the entanglement increase calculating the logarithmic negativity of the output state and discuss and compare the performance of the protocols.
We propose a scheme for purification and distillation of squeezed and entangled continuous-variable states of light transmitted through a channel exhibiting phase fluctuations. The outstanding advantage of the suggested protocol is its experimental feasibility since it only involves an interference of two copies of the decohered state on a balanced beam splitter, a homodyne measurement on one of the output beams, and a conditioning on the measurement outcome. The purification can counteract the detrimental effects of phase fluctuations in optical quantum-communication networks.
Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67, 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311, 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits of the two proposed detection schemes, namely photo-detection and homodyne detection, in the light of experimental realizations of this idea becoming more and more feasible.
Entanglement distillation aims at preparing highly entangled states out of a supply of weakly entangled pairs, using local devices and classical communication only. In this note we discuss the experimentally feasible schemes for optical continuous-variable entanglement distillation that have been presented in [D.E. Browne, J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. A 67 , 062320 (2003)] and [J. Eisert, D.E. Browne, S. Scheel, and M.B. Plenio, Annals of Physics (NY) 311 , 431 (2004)]. We emphasize their versatility in particular with regards to the detection process and discuss the merits of the two proposed detection schemes, namely photo-detection and homodyne detection, in the light of experimental realizations of this idea becoming more and more feasible.