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arXiv:1507.08171 · Physical Review Letters

Assisted Distillation of Quantum Coherence

Eric Chitambar, Alexander Streltsov, Swapan Rana, Manabendra Nath Bera, Gerardo Adesso, Maciej Lewenstein

Published Feb 17, 2016• 245 citations
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Abstract

We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.

DOI
10.1103/physrevlett.116.070402

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We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system, while general local quantum operations are permitted on the other; this is an operational paradigm that we call local quantum-incoherent operations and classical communication. We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the entanglement of assistance, whose properties we characterize. Our findings imply a novel interpretation of the von Neumann entropy: it quantifies the maximum amount of extra quantum coherence a system can gain when receiving assistance from a collaborative party. Our results are generalized to coherence localization in a multipartite setting and possible applications are discussed.
We obtain the general formula for the optimal rate on one of the subsystems that can be distilled from any bipartite quantum state by one-way local quantum-incoherent operations and classical communication. We provide lower and upper bounds on the assisted distillation of coherence using so-called one-shot entropies, and we establish a hierarchy of information quantities that can be used to calculate an assisted distillable rate in the asymptotical limit. We show that they asymptotically coincide with the quantum-incoherent relative entropy, and our findings imply a novel operational interpretation of quantum-incoherent relative entropy.
In the task of assisted coherence distillation via the set of operations X, where X is either local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), or separable quantum incoherent operations (SQI), two parties, namely Alice and Bob, share many copies of a bipartite joint state. The aim of the process is to generate the maximal possible coherence on the subsystem of Bob. In this paper, we investigate the assisted coherence distillation of some special mixed states, the states with vanished basis-dependent discord and Werner states. We show that all the four sets of operations are equivalent for assisted coherence distillation, whenever Alice and Bob share one of those mixed quantum states. Moreover, we prove that the assisted coherence distillation of the former can reach the upper bound, namely QI relative entropy, while that of the latter can not. Meanwhile, we also present a sufficient condition such that the assistance of Alice via the set of operations X can not help Bob improve his distillable coherence, and this condition is that the state shared by Alice and Bob has vanished basis-dependent discord.
Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. \textbf{116}, 070402 (2016)] studied the manipulation of quantum coherence in bipartite or multipartite systems under the protocol Local Incoherent Operation and Classical Communication (LQICC). Here we present the first experimental realization of obtaining maximal coherence in assisted distillation protocol based on linear optical system. The results of our work show that the optimal distillable coherence rate can be reached even in one-copy scenario when the overall bipartite qubit state is pure. Moreover, the experiments for mixed states showed that distillable coherence can be increased with less demand than entanglement distillation. Our work might be helpful in the remote quantum information processing and quantum control.
We give the first systematic study on the second order asymptotics of the operational task of coherence distillation with and without assistance. In the unassisted setting, we introduce a variant of randomness extraction framework where free incoherent operations are allowed before the incoherent measurement and the randomness extractors. We then show that the maximum number of random bits extractable from a given quantum state is precisely equal to the maximum number of coherent bits distillable from the same state. This relation enables us to derive tight second order expansions of both tasks in the independent and identically distributed setting. Remarkably, the incoherent operation classes that can empower coherence distillation for generic states all admit the same second order expansions, indicating their operational equivalence for coherence distillation in both asymptotic and large block length regimes. We then generalize the above line of research to the assisted setting, arising naturally in bipartite quantum systems where Bob distills coherence from the state at hand, aided by the benevolent Alice possessing the other system. More precisely, we introduce a new assisted incoherent randomness extraction task and establish an exact relation between this task and the assisted coherence distillation. It strengthens the one-shot relation in the unassisted setting and confirms that this cryptographic framework offers a new perspective to the study of quantum coherence distillation. Likewise, this relation yields second order characterizations to the assisted tasks. As by-products, we show the strong converse property of the tasks above from their second order expansions.
The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in general, we show that the larger class of separable incoherent operations (SI) has a simple mathematical form, yet still preserving the main features of LICC. We apply these results to the task of assisted coherence distillation, where the aim is to locally extract maximally coherent states. For all pure states and certain mixed states we observe a collapse of all classes: the distillation rate is always the same. It remains open if the distillation rate can be different for general mixed states, and if the intersection of LOCC and SI is equivalent to LICC. We also introduce the task of incoherent teleportation and show that perfect incoherent teleportation of one qubit is possible with one singlet and two bits of classical communication. The approach presented here opens new ways to study the resource theory of coherence in distributed scenarios.
We study the process of assisted work distillation. This scenario arises when two parties share a bipartite quantum state ρ_{AB} and their task is to locally distill the optimal amount of work when one party is restricted to thermal operations, whereas the other can perform general quantum operations and they are allowed to communicate classically. We demonstrate that this question is intimately related to the distillation of classical and quantum correlations. In particular, we show that the advantage of one party performing global measurements over many copies of ρ_{AB} is related to the nonadditivity of the entanglement of formation. We also show that there may exist work bound in the quantum correlations of the state that is only extractable under the wider class of local Gibbs-preserving operations.