Distributed quantum information processing is essential for building quantum networks and enabling more extensive quantum computations. In this regime, several spatially separated parties share a multipartite quantum system, and the most natural set of operations are Local Operations and Classical Communication (LOCC). As a pivotal part in quantum information theory and practice, LOCC has led to many vital protocols such as quantum teleportation. However, designing practical LOCC protocols is challenging due to LOCC’s intractable structure and limitations set by near-term quantum devices. Here we introduce LOCCNet, a machine learning framework facilitating protocol design and optimization for distributed quantum information processing tasks. As applications, we explore various quantum information tasks such as entanglement distillation, quantum state discrimination, and quantum channel simulation. We discover novel protocols with evident improvements, in particular, for entanglement distillation with quantum states of interest in quantum information. Our approach opens up new opportunities for exploring entanglement and its applications with machine learning, which will potentially sharpen our understanding of the power and limitations of LOCC.

Quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the rise of quantum information theory, it has been an open problem to quantify entanglement in an information-theoretically meaningful way. In particular, every previously defined entanglement measure bearing a precise information-theoretic meaning is not known to be efficiently computable, or if it is efficiently computable, then it is not known to have a precise information-theoretic meaning. In this Letter, we meet this challenge by introducing an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state when two distant parties are allowed to perform quantum operations that completely preserve the positivity of the partial transpose. Additionally, this entanglement measure is efficiently computable by means of a semidefinite program, and it bears a number of useful properties such as additivity and faithfulness. Our results bring key insights into the fundamental entanglement structure of arbitrary quantum states, and they can be used directly to assess and quantify the entanglement produced in quantum-physical experiments.

Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum “magic.” In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation.

We study the one-shot and asymptotic quantum communication assisted with the positive-partial-transpose-preserving (PPT) and no-signalling (NS) codes. We first show improved general semidefinite programming (SDP) finite blocklength converse bounds for quantum communication with a given infidelity tolerance and utilize them to study the depolarizing channel and amplitude damping channel in a small blocklength. Based on the one-shot bounds, we then derive a general SDP strong converse bound for the quantum capacity of an arbitrary quantum channel. In particular, we prove that the SDP strong converse bound is always smaller than or equal to the partial transposition bound introduced by Holevo and Werner, and the inequality could be strict. Furthermore, we show that the SDP strong converse bound can be refined as the max-Rains information, which is an analog to the Rains information introduced in [Tomamichel/Wilde/Winter, IEEE Trans. Inf. Theory 63:715, 2017]. This also implies that it is always no smaller than the Rains information. Finally, we establish an inequality relationship among some of these known strong converse bounds on quantum capacity.

We demonstrate the irreversibility of asymptotic entanglement manipulation under quantum operations that completely preserve positivity of partial transpose (PPT), which resolves a major open problem in quantum information theory. To be more specific, we show that for any rank-two mixed state supporting on the $3øtimes3$ antisymmetric subspace, the amount of distillable entanglement by PPT operations is strictly smaller than one entanglement bit (ebit) while its entanglement cost under PPT operations is exactly one ebit. As a byproduct, we find that for this class of quantum states, both the Rains' bound and its regularization, are strictly less than the asymptotic relative entropy of entanglement with respect to PPT states. So in general there is no unique entanglement measure for the manipulation of entanglement by PPT operations. We further present a feasible sufficient condition for the irreversibility of entanglement manipulation under PPT operations.