Postselected communication over quantum channels
arXiv:2308.02583 · doi:10.1142/S0219749924400124
Abstract
The single-letter characterisation of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, `inconclusive' measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterisation of postselected capacities in the setting of entanglement assistance as well as the more general nonsignalling assistance, establishing that they are both equal to the channel's projective mutual information -- a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation-based protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel's ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves.
38 pages, 5 figures, published in International Journal of Quantum Information (IJQI) as part of a special issue dedicated to Alexander S. Holevo on the occasion of his 80th birthday
References in corpus (51)
- Quantum Resource Theories
- Quantum Computational Supremacy
- Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
- Superadditivity of communication capacity using entangled inputs
- Min- and Max- Relative Entropies and a New Entanglement Monotone
- From Classical to Quantum Shannon Theory
- Quantum Communication With Zero-Capacity Channels
- Transforming quantum operations: quantum supermaps
- Quantum Reverse Shannon Theorem
- Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
- The Quantum Reverse Shannon Theorem based on One-Shot Information Theory
- Closed timelike curves via post-selection: theory and experimental demonstration
- Maximum Confidence Quantum Measurements
- Unambiguous discrimination of mixed states
- Quantum Advantage in Postselected Metrology
- Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
- Comparison of Quantum Channels by Superchannels
- Entanglement-Assisted Capacity of Quantum Multiple-Access Channels
- Optimum unambiguous discrimination of two mixed quantum states
- Optimal discrimination of mixed quantum states involving inconclusive results
- Approaches for approximate additivity of the Holevo information of quantum channels
- The quantum mechanics of time travel through post-selected teleportation
- On entanglement-assisted classical capacity
- Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
- Quantum limits on post-selected, probabilistic quantum metrology
- Entangled Mixed States and Local Purification
- One shot entanglement assisted classical and quantum communication over noisy quantum channels: A hypothesis testing and convex split approach
- Using and reusing coherence to realize quantum processes
- Gaussian bosonic synergy: quantum communication via realistic channels of zero quantum capacity
- On the power of PPT-preserving and non-signalling codes
- Principles of Quantum Communication Theory: A Modern Approach
- Application of the Resource Theory of Channels to Communication Scenarios
- Hilbert's projective metric in quantum information theory
- No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number
- Quantum Channel Simulation and the Channel's Smooth Max-Information
- On the Second-Order Asymptotics for Entanglement-Assisted Communication
- Probabilistic transformations of quantum resources
- Quantum Feedback Channels
- Applications of position-based coding to classical communication over quantum channels
- Error Exponents of Erasure/List Decoding Revisited via Moments of Distance Enumerators
- Tight constraints on probabilistic convertibility of quantum states
- Perfect state distinguishability and computational speedups with postselected closed timelike curves
- Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
- Optimal probabilistic estimation of quantum states
- Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels
- Beating noise with abstention in state estimation
- Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
- Necessary and Sufficient Conditions on Measurements of Quantum Channels
- Postselected quantum hypothesis testing
- Cost of postselection in decision theory
- Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses