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Register a new userOne-shot manipulation of entanglement for quantum channels
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We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesis-testing relative entropy of channels with minimization over separable channels. We also address the one-shot catalytic dynamic entanglement cost of a bipartite quantum channel under a larger class of free superchannels that could generate the dynamic entanglement which is asymptotically negligible; it is bounded by the generalized log-robustness of channels.
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We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate transformations in general resource theories. Our framework encompasses all dynamical resources represented as quantum channels, including those with a specific structure --- such as boxes, assemblages, and measurements --- thus immediately applying in a vast range of physical settings. For the particularly important manipulation tasks of distillation and dilution, we show that our conditions become necessary and sufficient for broad classes of important theories, enabling an exact characterization of these tasks and establishing a precise connection between operational problems and resource monotones based on entropic divergences. We exemplify our results by considering explicit applications to: quantum communication, where we obtain exact expressions for one-shot quantum capacity and simulation cost assisted by no-signalling, separability-preserving, and positive partial transpose-preserving codes; as well as to nonlocality, contextuality, and measurement incompatibility, where we present operational applications of a number of relevant resource measures.
We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation}, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard, Devetak and Hayden. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
We report a novel and simple approach for generating near-perfect quality polarization entanglement in a fully guided-wave fashion. Both deterministic pair separation into two adjacent telecommunication channels and the paired photons temporal walk-off compensation are achieved using standard fiber components. Two-photon interference experiments are performed, both for quantitatively demonstrating the relevance of our approach, and for manipulating the produced state between bosonic and fermionic symmetries. The compactness, versatility, and reliability of this configuration makes it a potential candidate for quantum communication applications.
Quantum channels, which break entanglement, incompatibility, or nonlocality, are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to certain temporal quantum correlations, i.e., temporal separability, channel unsteerability, temporal unsteerability, and macrorealism. More specifically, we first define the steerability-breaking channel, which is conceptually similar to the entanglement and nonlocality-breaking channels and prove that it is identical to the incompatibility-breaking channel. Similar to the hierarchy relations of the temporal and spatial quantum correlations, the hierarchy of non-breaking channels is discussed. We then introduce the concept of the channels which break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A certain measure of temporal nonseparability can be used to quantify a non-entanglement-breaking channel in the sense that the measure is a memory monotone under the framework of the resource theory of the quantum memory. (2) A non-steerability-breaking channel can be certified with channel steering because the steerability-breaking channel is equivalent to the incompatibility-breaking channel. (3) The temporal steerability and non-macrorealism can, respectively, distinguish the steerability-breaking and the nonlocality-breaking unital channel from their corresponding non-breaking channels. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to compare the temporal quantum correlations with non-breaking channels.
We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows for a straightforward comparison of their exact achievable performance, we relate the fidelity of distillation under these classes of operations with a family of entanglement monotones and the rates of distillation with a class of smoothed entropic quantities based on the hypothesis testing relative entropy. We then characterise exactly the one-shot distillable entanglement of several classes of quantum states and reveal many simplifications in their manipulation. We show in particular that the $varepsilon$-error one-shot distillable entanglement of any pure state is the same under all sets of operations ranging from one-way LOCC to separability-preserving operations or operations preserving the set of states with positive partial transpose, and can be computed exactly as a quadratically constrained linear program. We establish similar operational equivalences in the distillation of isotropic and maximally correlated states, reducing the computation of the relevant quantities to linear or semidefinite programs. We also show that all considered sets of operations achieve the same performance in environment-assisted entanglement distillation from any state.
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