Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement

Abstract

We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's pre-shared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a "witness". Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender's signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels our capacity formula has a simple closed-form. Moreover, our additive capacity formula upper bounds the general coherent attack's information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful.

5+7 pages

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• Superadditivity of the Classical Capacity with Limited Entanglement Assistance
• Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
• Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?
• Security-proof framework for two-way Gaussian quantum-key-distribution protocols
• Quantum-enabled communication without a phase reference
• Large-Alphabet Encoding Schemes for Floodlight Quantum Key Distribution
• High-order encoding schemes for floodlight quantum key distribution
• Every entangled state provides an advantage in classical communication
• Secure Quantum Pattern Communication
• Fault-tolerant Coding for Entanglement-Assisted Communication
• No-go theorem for environment-assisted invariance in non-unitary dynamics
• Permutation Enhances Classical Communication Assisted by Entangled States