Energy-constrained two-way assisted private and quantum capacities of quantum channels

Abstract

With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energy-constrained, LOCC-assisted private and quantum capacities of quantum channels, which are the maximum rates at which an LOCC-assisted quantum channel can reliably establish secret key or entanglement, respectively, subject to an energy constraint on the channel input states. We prove that the energy-constrained squashed entanglement of a channel is an upper bound on these capacities. We also explicitly prove that a thermal state maximizes a relaxation of the squashed entanglement of all phase-insensitive, single-mode input bosonic Gaussian channels, generalizing results from prior work. After doing so, we prove that a variation of the method introduced in [Goodenough et al., New J. Phys. 18, 063005 (2016)] leads to improved upper bounds on the energy-constrained secret-key-agreement capacity of a bosonic thermal channel. We then consider a multipartite setting and prove that two known multipartite generalizations of the squashed entanglement are in fact equal. We finally show that the energy-constrained, multipartite squashed entanglement plays a role in bounding the energy-constrained LOCC-assisted private and quantum capacity regions of quantum broadcast channels.

arXiv comment31 pages, 6 figures

References in corpus (52)

• Quantum entanglement
• Mixed State Entanglement and Quantum Error Correction
• The Security of Practical Quantum Key Distribution
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Continuous variable quantum cryptography using coherent states
• General Benchmarks for Quantum Repeaters
• Fundamental Limits of Repeaterless Quantum Communications
• Monogamy of entanglement and other correlations
• General Entanglement Breaking Channels
• Fundamental rate-loss tradeoff for optical quantum key distribution
• "Squashed Entanglement" - An Additive Entanglement Measure
• Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
• Secure key from bound entanglement
• Extremality of Gaussian quantum states
• Continuity of quantum conditional information
• Faithful Squashed Entanglement
• Quantum Capacities of Bosonic Channels
• Converse bounds for private communication over quantum channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• The exact cost of redistributing multipartite quantum states
• General paradigm for distilling classical key from quantum states
• Operator-sum Representation for Bosonic Gaussian Channels
• Optimal quantum source coding with quantum information at the encoder and decoder
• Quantum broadcast channels
• The squashed entanglement of a quantum channel
• Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
• Fundamental rate-loss tradeoff for the quantum internet
• Relative Entropy Bounds on Quantum, Private and Repeater Capacities
• Majorization theory approach to the Gaussian channel minimum entropy conjecture
• Parameter regimes for a single sequential quantum repeater
• Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
• Multipartite Classical and Quantum Secrecy Monotones
• Fundamental limitation on quantum broadcast networks
• Amortized entanglement of a quantum channel and approximately teleportation-simulable channels
• Assessing the performance of quantum repeaters for all phase-insensitive Gaussian bosonic channels
• Measures of quantum correlations in infinite-dimensional systems
• Versatile relative entropy bounds for quantum networks
• Upper bounds on secret key agreement over lossy thermal bosonic channels
• The entropy gain of infinite-dimensional quantum channels
• The classical capacity of quantum thermal noise channels to within 1.45 bits
• Quantum conditional entropy for infinite-dimensional systems
• Distributed Compression and Multiparty Squashed Entanglement
• Squashed entanglement and approximate private states
• Amortization does not enhance the max-Rains information of a quantum channel
• Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels
• Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
• Squashed entanglement in infinite dimensions
• Infinite Shannon entropy
• Quantum states representing perfectly secure bits are always distillable
• Strong converse rates for classical communication over thermal and additive noise bosonic channels
• Entanglement-assisted capacity of constrained quantum channel
• Strong converse for the classical capacity of optical quantum communication channels

Cited by in corpus (16)

• Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission
• Narrow Bounds for the Quantum Capacity of Thermal Attenuators
• Comparison of Discrete Variable and Continuous Variable Quantum Key Distribution Protocols with Phase Noise in the Thermal-Loss Channel
• Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities
• Quantum communication on the bosonic loss-dephasing channel
• Quantum Channel Capacities Per Unit Cost
• Entanglement catalysis for quantum states and noisy channels
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Multipartite Optimized Correlation Measures and Holography
• Optical fibres with memory effects and their quantum communication capacities
• On lower semicontinuity of the quantum conditional mutual information and its corollaries
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
• The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
• Information-theoretic aspects of the generalized amplitude damping channel
• Squashed Entanglement from Generalized Rindler Wedge
• Energy-limited quantum dynamics