No-Signalling Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovasz Number

Understand

We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one.

• Quantum no-signalling correlations are viewed as two-input and two-output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal.
• Both problems lead to simple semidefinite programmes (SDPs) that depend only on the Kraus operator space of the channel.
• In particular, we show that the zero-error classical simulation cost is precisely the conditional min-entropy of the Choi-Jamiolkowski matrix of the given channel.