Approximate quasi-orthogonality of operator algebras and relative quantum privacy. Issue 2 (April 2021)

• Record Type: Journal Article
• Authors: Kribs, David W.; Levick, Jeremy; Nelson, Mike; Pereira, Rajesh; Rahaman, Mizanur
• Is Part Of: Reports on mathematical physics. Volume 87:Issue 2(2021)
• Page Start: 167
• Page End: 181
• Publication Date: 2021-04
• Subjects: completely positive map -- private quantum channel -- conditional expectation -- operator algebra -- private quantum code -- quasi-orthogonal algebra; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(21)00024-0
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : We show that the approximate quasi-orthogonality 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.