Trace distance from the viewpoint of quantum operation techniques

Abstract

In the present paper, the trace distance is exposed within the quantum operations formalism. The definition of the trace distance in terms of a maximum over all quantum operations is given. It is shown that for any pair of different states, there are an uncountably infinite number of maximizing quantum operations. Conversely, for any operation of the described type, there are an uncountably infinite number of those pairs of states that the maximum is reached by the operation. A behavior of the trace distance under considered operations is studied. Relations and distinctions between the trace distance and the sine distance are discussed.

26 pages, no figures. The bibliography is extended, explanatory improvements

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Cited by in corpus (7)

• Maximally entangled mixed states for qubit-qutrit systems
• Partitioned trace distances
• Minimal time required to charge a quantum system
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Bounds on Shannon distinguishability in terms of partitioned measures
• Unconditionally Secure Commitments with Quantum Auxiliary Inputs
• A Note on Output Length of One-Way State Generators and EFIs