Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
arXiv:1808.01498 · doi:10.1007/s11005-020-01297-7
Abstract
It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi [IEEE Trans. Inf. Theory 55(8), 3807 (2009)] showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein's lemma for classical-quantum channels by showing that asymptotically the exponential error rate for classical-quantum channel discrimination is not improved by adaptive strategies. Second, we recover many other classes of channels for which adaptive strategies do not lead to an asymptotic advantage. Third, we give various converse bounds on the power of adaptive protocols for general asymptotic quantum channel discrimination. Intriguingly, it remains open whether adaptive protocols can improve the exponential error rate for quantum channel discrimination in the asymmetric Stein setting. Our proofs are based on the concept of amortized distinguishability of quantum channels, which we analyse using data-processing inequalities.
arXiv commentv2: 55 pages, 4 figures, final version published in Letters in Mathematical Physics
References in corpus (71)
- Quantum Resource Theories
- On quantum Renyi entropies: a new generalization and some properties
- Distance measures to compare real and ideal quantum processes
- Superadditivity of communication capacity using entangled inputs
- The Quantum Chernoff Bound
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- From Classical to Quantum Shannon Theory
- Quantum Circuits Architecture
- Using entanglement against noise in quantum metrology
- Programmable quantum gate arrays
- Codes for the Quantum Erasure Channel
- Transforming quantum operations: quantum supermaps
- Statistical distinguishability between unitary operations
- Asymptotic Error Rates in Quantum Hypothesis Testing
- The Chernoff lower bound for symmetric quantum hypothesis testing
- Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- Memory effects in quantum channel discrimination
- On the capacities of bipartite Hamiltonians and unitary gates
- alpha-z-relative Renyi entropies
- Toward a general theory of quantum games
- Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
- Comparison of Quantum Channels by Superchannels
- The Perfect Distinguishability of Quantum Operations
- Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations
- Fundamental limits to quantum channel discrimination
- Equivalence of wave-particle duality to entropic uncertainty
- Approaches for approximate additivity of the Holevo information of quantum channels
- Adaptive versus non-adaptive strategies for quantum channel discrimination
- Fundamental bound on the reliability of quantum information transmission
- On the strong converses for the quantum channel capacity theorems
- Ultimate Precision of Adaptive Noise Estimation
- Gaussian hypothesis testing and quantum illumination
- Strong converse exponent for classical-quantum channel coding
- Discrimination of two channels by adaptive methods and its application to quantum system
- Using and reusing coherence to realize quantum processes
- Optimal Entanglement Generation from Quantum Operations
- Multiplicativity of completely bounded -norms implies a strong converse for entanglement-assisted capacity
- Multiplicativity of completely bounded p-norms implies a new additivity result
- On the power of PPT-preserving and non-signalling codes
- Relative Entropy Bounds on Quantum, Private and Repeater Capacities
- The Converse Part of The Theorem for Quantum Hoeffding Bound
- The minimum error probability of quantum illumination
- Quantum Relative Lorenz Curves
- Energy-constrained diamond norms and their use in quantum information theory
- Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
- Identification and Distance Measures of Measurement Apparatus
- Discriminating quantum states: the multiple Chernoff distance
- Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
- Semidefinite programming converse bounds for quantum communication
- Sine distance for quantum states
- On a measure of distance for quantum strategies
- Quantum speedup in the identification of cause-effect relations
- Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
- Realization schemes for quantum instruments in finite dimensions
- Lower bound on the relative error of mixed-state cloning and related operations
- Strategies for optimal single-shot discrimination of quantum measurements
- Upper bounds on secret key agreement over lossy thermal bosonic channels
- Amortization does not enhance the max-Rains information of a quantum channel
- Almost all quantum channels are equidistant
- Relative entropies of quantum channels with applications in resource theory
- Parallel distinguishability of quantum operations
- Pretty good measures in quantum information theory
- Continuity bounds for information characteristics of quantum channels depending on input dimension
- Uniform continuity bounds for information characteristics of quantum channels depending on input dimension and on input energy
- Optimal estimation and discrimination of excess noise in thermal and amplifier channels
- Quantum Strategies and Local Operations
- Quantum reading capacity: General definition and bounds
- Ancilla dimension in quantum channel discrimination
- Programmable quantum channels and measurements
Cited by in corpus (69)
- Comparison of Quantum Channels by Superchannels
- Quantifying the magic of quantum channels
- Fundamental limits of quantum illumination
- Asymptotic theory of quantum channel estimation
- A chain rule for the quantum relative entropy
- Quantum Channel Simulation and the Channel's Smooth Max-Information
- Fundamental limitations on distillation of quantum channel resources
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Entropy of a quantum channel
- Physical Implementability of Linear Maps and Its Application in Error Mitigation
- No-go theorems for quantum resource purification II: new approach and channel theory
- Geometric distinguishability measures limit quantum channel estimation and discrimination
- On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources
- Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
- Defining quantum divergences via convex optimization
- On contraction coefficients, partial orders and approximation of capacities for quantum channels
- Quantifying dynamical magic with completely stabilizer preserving operations as free
- Usefulness of adaptive strategies in asymptotic quantum channel discrimination
- Quantum Rényi and -divergences from integral representations
- Quantum data hiding with continuous variable systems
- Ultimate limits for quickest quantum change-point detection
- Uniqueness and Optimality of Dynamical Extensions of Divergences
- Bounding the forward classical capacity of bipartite quantum channels
- Quantum metrology in the finite-sample regime
- Exact quantum sensing limits for bosonic dephasing channels
- Quantum-machine-learning channel discrimination
- Quantum rebound capacity
- Discrimination of POVMs with rank-one effects
- Postselected quantum hypothesis testing
- Some continuity properties of quantum Rényi divergences
- Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
- Quantum Bell Nonlocality is Entanglement
- Finding the optimal probe state for multiparameter quantum metrology using conic programming
- Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
- Exact entanglement cost of quantum states and channels under PPT-preserving operations
- Evaluating the Advantage of Adaptive Strategies for Quantum Channel Distinguishability
- A hierarchy of efficient bounds on quantum capacities exploiting symmetry
- RLD Fisher Information Bound for Multiparameter Estimation of Quantum Channels
- Continuity of entropies via integral representations
- Complexity in algebraic QFT
- Quantum Network Discrimination
- Infinite-Dimensional Programmable Quantum Processors
- Computable lower bounds on the entanglement cost of quantum channels
- Locally-Measured Rényi Divergences
- Transmission distance in the space of quantum channels
- Cone-Restricted Information Theory
- Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
- One-shot manipulation of coherence in dynamic quantum resource theory
- Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback
- Projective robustness for quantum channels and measurements and their operational significance
- On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
- Chain rules for quantum channels
- Postselected communication over quantum channels
- Choi-Defined Resource Theories
- Excluding false negative error in certification of quantum channels
- Adversarial quantum channel discrimination
- Towards the ultimate limits of quantum channel discrimination and quantum communication
- Indefinite causal order strategy does not improve the estimation of group action
- Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
- Extendibility limits quantum-secured communication and key distillation
- Entropic and operational characterizations of dynamic quantum resources
- Weight-based measure of quantum memory as a universal and operational benchmark
- Asymptotic Equipartition Theorems in von Neumann algebras
- Discrimination and certification of unknown quantum measurements
- Retrocausal capacity of a quantum channel: Communicating through noisy closed timelike curves
- Fast tests for probing the causal structure of quantum processes
- Optimal Hamiltonian recognition of unknown quantum dynamics
- Bayesian and Markovian classical feedforward for discriminating qubit channels
- Bounding the benefit of adaptivity in quantum metrology using the relative fidelity