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.
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.
Recently Horodecki et al. [Phys. Rev. Lett. 90, 100402 (2003)] introduced an important quantum information processing paradigm in which two parties sharing many copies of the same bipartite quantum state distill local pure states by means of local unitary operations assisted by a one-way (two-way) completely dephasing channel. Local pure states are a valuable resource from a thermodynamical point of view since they allow thermal energy to be converted into work by local quantum heat engines. The work deficit was defined as the decrease in the work extractable from the joint system due to this process of localization, and was proposed as a measure of the quantumness of correlations. We give a simple information theoretical characterization of the one-way work deficit, which turns out to be complementary to a previously known operational measure of classical correlations, the one-way distillable common randomness
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.
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.
In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party increases the amount of local resource with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-known case of entanglement theory, two-way classical communication does not lead to any improvement over one-way classical communication from the aiding party to the aided party. We then provide a concise general expression for the Gaussian resource of assistance, i.e., the maximum amount of resource that can be obtained when the aiding party holds a purification of the aided party's state, as measured by a general monotone. To demonstrate its usefulness, we apply our result to two important kinds of resources, squeezing and entanglement, and find some simple analytic solutions. In the case of entanglement theory, we are able to find general upper bounds on the regularized Gaussian entanglement of assistance, and to establish additivity for tensor powers of thermal states. This allows us to draw a quantitative and enlightening comparison with the performance of assisted entanglement distillation in the non-Gaussian setting. On the technical side, we develop some variational expressions to handle functions of symplectic eigenvalues that may be of independent interest. Our results suggest further potential for Gaussian operations to play a major role in practical quantum information processing protocols.
In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party distills resources with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-known case of entanglement theory, two-way classical communication does not lead to any improvement over one-way classical communication from the aiding party to the aided party. We then provide a concise general expression for the Gaussian resource of assistance, i.e., the distillable resource when the aiding party holds a purification of the aided party's state. To demonstrate the usefulness of this general expression, we apply it to two important kinds of resources, squeezing and entanglement, and find some simple analytic solutions. In the case of entanglement theory, we are able to find general upper bounds on the regularized Gaussian entanglement of assistance, and to establish additivity for tensor powers of thermal states. This allows us to draw a quantitative and enlightening comparison with the performance of assisted entanglement distillation in the non-Gaussian setting. On the technical side, we develop some variational expressions to handle functions of symplectic eigenvalues that may be of independent interest. Our results suggest further potential for Gaussian operations to play a major role in practical quantum information processing protocols.
We investigate the problem of producing local pure states by performing local noisy operations assisted by one-way classical communication on a given bipartite mixed state in the one-shot setting. We consider the following two scenarios:1)Scenario I: A party, say Alice, is provided with a single copy of some quantum state ρAon system A. The task for Alice is to extract pure qubit states using only noisy operations on A. We call this task purity concentration.2)Scenario II: Two parties, Alice and Bob possess the A and B sub-systems, respectively, of a given bipartite quantum state ρAB. They are allowed to perform any local noisy operations and communicate via a one-way dephasing (i.e., classical) channel. The task for them is to design a protocol using these resources such that together they can extract pure local qubit states from the shared state ρAB. We call this task local purity distillation.