Entangled inputs cannot make imperfect quantum channels perfect

Abstract

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.

5 pages, 2 figures, an error in the argument on the quantum capacity corrected, version to be published in the Physical Review Letters

References in corpus (2)

• Relative Entropy of Entanglement and Restricted Measurements
• Highly Entangled States With Almost No Secrecy

Cited by in corpus (15)

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• Semidefinite programming strong converse bounds for classical capacity
• Chaos-driven dynamics in spin-orbit coupled atomic gases
• Potential capacities of quantum channels
• Quantum Channel Capacities with Passive Environment Assistance
• Entropic singularities give rise to quantum transmission
• Pursuing the fundamental limits for quantum communication
• Preserving Information from the Beginning to the End of time in a Robertson-Walker Spacetime
• The minimum entropy output of a quantum channel is locally additive
• Beating the Classical Limits of Information Transmission using a Quantum Decoder
• Additivity rates and PPT property for random quantum channels
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• Parrondo's paradox and superactivation of classical and quantum capacity of communication channels with memory
• The minimum Renyi entropy output of a quantum channel is locally additive