2020/04/30 by Huaixin Cao, Yuxing Du, Cao, Huaixin +7
Computer Science · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2004.14540
Since masking of quantum information was introduced by Modi et al. in [PRL 120, 230501 (2018)], many discussions on this topic have been published. In this paper, we consider relationship between quantum multipartite maskers (QMMs) and quantum error-correcting codes (QECCs). We say that a subset Q of pure states of a system K can be masked by an operator S into a multipartite system \H(n) if all of the image states S|ψ> of states |ψ> in Q have the same marginal states on each subsystem. We call such an S a QMM of Q. By establishing an expression of a QMM, we obtain a relationship between QMMs and QECCs, which reads that an isometry 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 an isometric universal masker from \C2 into \C2⊗\C2⊗\C2 and then the states of \C3 can not be masked isometrically into \C2⊗\C2⊗\C2. This gives a consummation to a main result and leads to a negative answer to an open question in [PRA 98, 062306 (2018)]. Another application is that arbitrary quantum states of \Cd can be completely hidden in correlations between any two subsystems of the tripartite system \Cd+1⊗\Cd+1⊗\Cd+1, while arbitrary quantum states cannot be completely hidden in the correlations between subsystems of a bipartite system [PRL 98, 080502 (2007)].