Strong converse rates for quantum communication

Abstract

We revisit a fundamental open problem in quantum information theory, namely whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here we establish that the Rains information of any quantum channel is a strong converse rate for quantum communication: For any sequence of codes with rate exceeding the Rains information of the channel, we show that the fidelity vanishes exponentially fast as the number of channel uses increases. This remains true even if we consider codes that perform classical post-processing on the transmitted quantum data. As an application of this result, for generalized dephasing channels we show that the Rains information is also achievable, and thereby establish the strong converse property for quantum communication over such channels. Thus we conclusively settle the strong converse question for a class of quantum channels that have a non-trivial quantum capacity.

v4: 13 pages, accepted for publication in IEEE Transactions on Information Theory

References in corpus (9)

• Coding Theorem and Strong Converse for Quantum Channels
• Post-selection technique for quantum channels with applications to quantum cryptography
• The quantum capacity with symmetric side channels
• Relating different quantum generalizations of the conditional Renyi entropy
• Renyi generalizations of the conditional quantum mutual information
• Quantum Coding with Finite Resources
• On the Second-Order Asymptotics for Entanglement-Assisted Communication
• Second-order asymptotics for source coding, dense coding and pure-state entanglement conversions
• Additive Extensions of a Quantum Channel

Cited by in corpus (54)

• Converse bounds for private communication over quantum channels
• Quantifying the magic of quantum channels
• Approaches for approximate additivity of the Holevo information of quantum channels
• Efficiently computable bounds for magic state distillation
• Renyi generalizations of the conditional quantum mutual information
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Semidefinite programming relaxations for quantum correlations
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Fundamental limitations on distillation of quantum channel resources
• Entropy of a quantum channel
• Entanglement cost and quantum channel simulation
• Semidefinite programming converse bounds for quantum communication
• Geometric distinguishability measures limit quantum channel estimation and discrimination
• Rényi divergences as weighted non-commutative vector valued $L_p$-spaces
• Optimized quantum f-divergences and data processing
• Positivity of linear maps under tensor powers
• Fundamental limits on the capacities of bipartite quantum interactions
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Causal limit on quantum communication
• Amortization does not enhance the max-Rains information of a quantum channel
• Exact solution for the quantum and private capacities of bosonic dephasing channels
• Renyi relative entropies of quantum Gaussian states
• Nonadditivity of Rains' bound for distillable entanglement
• Secret key distillation across a quantum wiretap channel under restricted eavesdropping
• On converse bounds for classical communication over quantum channels
• $\alpha$-Logarithmic negativity
• Continuity of quantum entropic quantities via almost convexity
• Pursuing the fundamental limits for quantum communication
• Sandwiched Rényi Convergence for Quantum Evolutions
• Resource theory of unextendibility and non-asymptotic quantum capacity
• Capacity Estimates via comparison with TRO channels
• Reversibility of quantum resources through probabilistic protocols
• Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels
• Recoverability for optimized quantum $f$-divergences
• The platypus of the quantum channel zoo
• Resonant Multilevel Amplitude Damping Channels
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
• Refined Strong Converse for the Constant Composition Codes
• Relative entropy of steering: On its definition and properties
• Exact entanglement cost of quantum states and channels under PPT-preserving operations
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Estimate distillable entanglement and quantum capacity by squeezing useless entanglement
• Quantum resource theory of coding for error correction
• Trade-offs on number and phase shift resilience in bosonic quantum codes
• Quantifying the unextendibility of entanglement
• Capacity Bounds via Operator Space Methods
• A smallest computable entanglement monotone
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Information-theoretic aspects of the generalized amplitude damping channel
• Second Law of Entanglement Dynamics for the Non-Asymptotic Regime
• Bipartite quantum states admitting a causal explanation
• Information storage and transmission under Markovian noise
• An additive refinement of quantum channel capacities