Time reversal and exchange symmetries of unitary gate capacities

Abstract

Unitary gates are an interesting resource for quantum communication in part because they are always invertible and are intrinsically bidirectional. This paper explores these two symmetries: time-reversal and exchange of Alice and Bob. We will present examples of unitary gates that exhibit dramatic separations between forward and backward capacities (even when the back communication is assisted by free entanglement) and between entanglement-assisted and unassisted capacities, among many others. Along the way, we will give a general time-reversal rule for relating the capacities of a unitary gate and its inverse that will explain why previous attempts at finding asymmetric capacities failed. Finally, we will see how the ability to erase quantum information and destroy entanglement can be a valuable resource for quantum communication.

17 pages. v2: improved bounds, clarified proofs. v3: published version, added section explaining notation

References in corpus (8)

• Quantum information can be negative
• Coding Theorem and Strong Converse for Quantum Channels
• A Resource Framework for Quantum Shannon Theory
• Implausible Consequences of Superstrong Nonlocality
• A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
• The entangling and disentangling power of unitary transformations are unequal
• Quantifying the resource of sharing a reference frame
• Relation between classical communication capacity and entanglement capability for two-qubit unitary operations

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