Semidefinite programming strong converse bounds for classical capacity

Abstract

We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the one-shot $\epsilon$-error capacity are formalized as semidefinite programs (SDPs). Based on this, we obtain improved SDP finite blocklength converse bounds of general quantum channels for entanglement-assisted codes and unassisted codes. Furthermore, we derive two SDP strong converse bounds for the classical capacity of general quantum channels: for any code with a rate exceeding either of the two bounds of the channel, the success probability vanishes exponentially fast as the number of channel uses increases. In particular, applying our efficiently computable bounds, we derive an improved upper bound on the classical capacity of the amplitude damping channel. We also establish the strong converse property for the classical and private capacities of a new class of quantum channels. We finally study the zero-error setting and provide efficiently computable upper bounds on the one-shot zero-error capacity of a general quantum channel.

26 pages; v2, v3 updated reference and results; v4 published in IEEE Transactions on Information Theory

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• Semidefinite programming relaxations for quantum correlations
• Entanglement of a bipartite channel
• Fundamental limitations on distillation of quantum channel resources
• Non-asymptotic entanglement distillation
• Semidefinite programming converse bounds for quantum communication
• Defining quantum divergences via convex optimization
• Quantum Channel Marginal Problem
• On converse bounds for classical communication over quantum channels
• Semidefinite programming hierarchies for constrained bilinear optimization
• Generic nonadditivity of quantum capacity in simple channels
• Pursuing the fundamental limits for quantum communication
• The Communication Value of a Quantum Channel
• Bounding the forward classical capacity of bipartite quantum channels
• Variational Quantum Algorithms for Semidefinite Programming
• The platypus of the quantum channel zoo
• Bounding quantum capacities via partial orders and complementarity
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Quantifying the performance of approximate teleportation and quantum error correction via symmetric two-PPT-extendibility
• Separation between quantum Lovász number and entanglement-assisted zero-error classical capacity
• Lower and upper bounds on nonunital qubit channel capacities
• Degradability of Fermionic Gaussian Channels
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• The noisy Werner-Holevo channel and its properties
• Upper Bounds on the Distillable Randomness of Bipartite Quantum States
• Moderate Deviation Analysis for Classical-Quantum Channels and Quantum Hypothesis Testing
• Computable entanglement cost under positive partial transpose operations
• Shadow Simulation of Quantum Processes
• Optimality of meta-converse for channel simulation
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Capacities of a two-parameter family of noisy Werner-Holevo channels
• Information-theoretic aspects of the generalized amplitude damping channel
• Converse bounds for classical communication over quantum networks
• Extendible quantum measurements and limitations on classical communication
• Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
• Joint Power and User Grouping Optimization in Cell-Free Massive MIMO Systems
• Tripartite-to-bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces
• Information storage and transmission under Markovian noise