Quantum multipartite maskers vs. quantum error-correcting codes

School of Mathematics and Information Science, Shaanxi Normal University - Xi'an 710119, China

^(a) guozhihua@snnu.edu.cn (corresponding author)
^(b) caohx@snnu.edu.cn (corresponding author)

Received: 9 June 2020
Accepted: 6 July 2020

Abstract

Since masking of quantum information was introduced by Modi et al. in Modi K. et al., Phys. Rev. Lett., 120 (2018) 230501, many discussions on this topic have been published. In this paper, we explore the relationship between quantum multipartite maskers (QMMs) and quantum error-correcting codes (QECCs). We say that a subset Q of pure states of a system can be masked by an operator S into a multipartite system if all of the image states of states in Q have the same marginal states on each subsystem. We call such an S a QMM of Q. By establishing a necessary and sufficient condition for a set Q to be masked by an operator, we prove that a linear operator is a QMM of all pure states of a system if and only if its range is a QECC of any one-erasure channel. As an application, we prove that there is no universal maskers from into and then the states of cannot be masked into . This gives a consummation to a main result and leads to a negative answer to an open question in Li M.‐S. and Wang Y.‐L., Phys. Rev. A, 98 (2018) 062306. Another application is that arbitrary quantum states of can be completely hidden in correlations between any two subsystems of the tripartite system , while arbitrary quantum states cannot be completely hidden in the correlations between subsystems of a bipartite system (Braunstein S. L. and Pati A. K., Phys. Rev. Lett., 98 (2007) 080502).