Amortization does not enhance the max-Rains information of a quantum channel

Abstract

Given an entanglement measure $E$, the entanglement of a quantum channel is defined as the largest amount of entanglement $E$ that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement $E$ that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and a channel's max-Rains information, found recently in [Wang et al., arXiv:1709.00200]. The main application of our result is a single-letter, strong-converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.

v2: 24 pages, 1 figure, final version accepted for publication in New Journal of Physics

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• Nonlocal Entanglement Transformations Achievable by Separable Operations
• Quantum Proofs
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Unconditional privacy over channels which cannot convey quantum information
• Versatile relative entropy bounds for quantum networks

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• Geometric distinguishability measures limit quantum channel estimation and discrimination
• Fundamental limits on the capacities of bipartite quantum interactions
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Causal limit on quantum communication
• Defining quantum divergences via convex optimization
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Pursuing the fundamental limits for quantum communication
• Resource theory of unextendibility and non-asymptotic quantum capacity
• Bounding the forward classical capacity of bipartite quantum channels
• Quantifying the performance of approximate teleportation and quantum error correction via symmetric two-PPT-extendibility
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Exact entanglement cost of quantum states and channels under PPT-preserving operations
• A hierarchy of efficient bounds on quantum capacities exploiting symmetry
• Computable lower bounds on the entanglement cost of quantum channels
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Information-theoretic aspects of the generalized amplitude damping channel
• Unextendible entanglement of quantum channels
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• Information storage and transmission under Markovian noise