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arXiv:1303.4978 · Physical Review A

Amendable Gaussian channels: Restoring entanglement via a unitary filter

Antonella De Pasquale, Andrea Mari, A. Porzio, Vittorio Giovannetti

Published Jun 7, 2013• 11 citations
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Abstract

We show that there exist Gaussian channels which are amendable. A channel that is entanglement-breaking of order 2 [A. De Pasquale and V. Giovannetti, Phys. Rev. A 86, 052302 (2012)] is amendable if there exists an unitary filter that, once applied in between two actions of the channel, removes the entanglement-breaking property of the overall transformation. We find that, depending on the structure of the channel, the unitary filter can be a squeezing transformation or a phase-shift operation. We also propose two realistic quantum optics experiments where the amendability of Gaussian channels can be verified by exploiting the fact that it is sufficient to test the entanglement-breaking properties of two-mode Gaussian channels on input states with finite energy (which are not maximally entangled).

DOI
10.1103/physreva.87.062307

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We show that there exist Gaussian channels which are amendable. A channel that is entanglement-breaking of order 2 [A. De Pasquale and V. Giovannetti, Phys. Rev. A 86, 052302 (2012)] is amendable if there exists an unitary filter that, once applied in between two actions of the channel, removes the entanglement-breaking property of the overall transformation. We find that, depending on the structure of the channel, the unitary filter can be a squeezing transformation or a phase-shift operation. We also propose two realistic quantum optics experiments where the amendability of Gaussian channels can be verified by exploiting the fact that it is sufficient to test the entanglement-breaking properties of two-mode Gaussian channels on input states with finite energy (which are not maximally entangled).
We propose a quantum optics experiment where a single two-mode Gaussian entangled state is used for realizing the paradigm of an amendable Gaussian channel recently presented in Phys. Rev. A, \textbf{87}, 062307 (2013). Depending on the choice of the experimental parameters the entanglement of the probe state is preserved or not and the relative map belongs or not to the class of entanglement breaking channels. The scheme has been optimized to be as simple as possible: it requires only a single active non-linear operation followed by four passive beam-splitters. The effects of losses, detection inefficiencies and statistical errors are also taken into account, proving the feasibility of the experiment with current realistic resources.
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase-damping or rotated amplitude-damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve entanglement transmission. This proof-of-principle demonstration could be generalized to many other physical scenarios where entanglement-breaking communication lines may be amended by unitary filters.
We study a set of new functionals (called entanglement–breaking indices) which characterize how many local iterations of a given (local) quantum channel are needed in order to completely destroy the entanglement between the system of interest over which the transformation is defined and an external ancilla. The possibility of contrasting the noisy effects introduced by the channel iterations via the action of intermediate (filtering) transformations is analyzed. We provide some examples in which our functionals can be exactly calculated. The differences between unitary and non-unitary filtering operations are analyzed showing that, at least for systems of dimension d larger than or equal to 3, the non-unitary choice is preferable (the gap between the performances of the two cases being divergent in some cases). For d = 2 (qubit case), on the contrary, no evidences of the presence of such gap is revealed: we conjecture that for this special case unitary filtering transformations are optimal. The scenario in which more general filtering protocols are allowed is also discussed in some detail. The case of a depolarizing noise acting on a two–qubit system is exactly solved in a general case.
We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by Browne et al. [Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy degaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.
Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low, or the thermal noise is high. This means that we can transmit quantum information reliably through very noisy Gaussian channels with the help of another Gaussian channel, whose quantum capacity is also zero. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the nonactivation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.