Pursuing the fundamental limits for quantum communication

Abstract

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.

14 pages, v3 close to the published version

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Cited by in corpus (12)

• Five Facets of 6G: Research Challenges and Opportunities
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Estimating Quantum and Private capacities of Gaussian channels via degradable extensions
• Generic nonadditivity of quantum capacity in simple channels
• Bounding quantum capacities via partial orders and complementarity
• Estimate distillable entanglement and quantum capacity by squeezing useless entanglement
• Bounding the quantum capacity with flagged extensions
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Additivity of quantum capacities in simple non-degradable quantum channels
• Testing identity of collections of quantum states: sample complexity analysis
• Dynamic LOCC Circuits for Automated Entanglement Manipulation