Year: 2026
Type: article
Abstract: We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system undergoing noise is NP-hard. This contrasts with the classical analogue of this problem that can clearly be solved efficiently. We also establish the NP-hardness of deciding if the contraction coefficient is equal to 1, i.e., the channel can perfectly preserve a bit. As a consequence, deciding if a non-commutative graph has an independence number of at least 2 is NP-hard. In addition, we establish a converging hierarchy of semidefinite programming upper bounds on the contraction coefficient.
Institutions: Lyon 1 Université, École Normale Supérieure de Lyon, Laboratoire de l'Informatique du Parallélisme, QINFO: Traitement optimal de l'information avec des dispositifs quantiques, Laboratoire Traitement et Communication de l’Information, QURIOSITY: Communication et Traitement Quantiques de l'Information, University of British Columbia
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: H2020 European Research Council
OpenAlex ID: W4414426786
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