Quantum Privacy and Schur Product Channels

Abstract

We investigate the quantum privacy properties of an important class of quantum chan-nels, by making use of a connection with Schur product matrix operations and associated correlationmatrix structures. For channels implemented by mutually commuting unitaries, which cannot priva-tise qubits encoded directly into subspaces, we nevertheless identify private algebras and subsystemsthat can be privatised by the channels. We also obtain further results by combining our analysiswith tools from the theory of quasiorthogonal operator algebras and graph theory.

11 pages

References in corpus (5)

• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Random subspaces for encryption based on a private shared Cartesian frame
• Private algebras in quantum information and infinite-dimensional complementarity
• Quantum Subsystems: Exploring the Complementarity of Quantum Privacy and Error Correction
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Cited by in corpus (7)

• Distinguishing classically indistinguishable states and channels
• Entanglement Breaking Channels, Stochastic Matrices, and Primitivity
• Quantum teleportation in the commuting operator framework
• Operator Algebra Generalization of a Theorem of Watrous and Mixed Unitary Quantum Channels
• Certifying nonlocal properties of noisy quantum operations
• Dephasing superchannels
• Structure Theorem for Quantum Replacer Codes