Quantum Wasserstein distance of order 1 between channels

Abstract

We set up a general theory for a quantum Wasserstein distance of order 1 in an operator algebraic framework, extending recent work in finite dimensions. In addition, this theory applies not only to states, but also to channels, giving a metric on the set of channels from one composite system to another. The additivity and stability properties of this metric are studied.

v1: 34 pages. v2: Minor changes and corrections. v3: Minor corrections; several references added. 35 pages

References in corpus (1)

• Quantum channels and their entropic characteristics

Cited by in corpus (4)

• Quantum Optimal Transport: Quantum Channels and Qubits
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Order $p$ quantum Wasserstein distances from couplings
• Quantum Wasserstein distance between unitary operations