Approximate Quasiorthogonality of Operator Algebras and Relative Quantum Privacy

TL;DR

This paper establishes a link between approximate quasiorthogonality of operator algebras and their approximate privacy in quantum channels, using Choi matrices and Kraus operators, with applications in quantum information.

Contribution

It introduces a new characterization of approximate quasiorthogonality via Choi matrices and Kraus operators, connecting it to quantum privacy.

Findings

Approximate quasiorthogonality is equivalent to approximate privacy in quantum channels.

Characterization of orthogonality measure using Choi matrices and Kraus operators.

Provides examples from various quantum information contexts.

Abstract

We show that the approximate quasiorthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum channels. Our analysis is based on a characterization of the measure of orthogonality in terms of Choi matrices and Kraus operators for completely positive maps. We present examples drawn from different areas of quantum information.