Masking quantum information encoded in pure and mixed states

TL;DR

This paper investigates the limits and possibilities of masking quantum information in pure and mixed states, establishing new conditions and constructions for what sets of states can be masked and confirming a previous conjecture.

Contribution

It provides necessary and sufficient conditions for masking pure states, constructs explicit maskers, and extends the concept of masking to mixed states with new results.

Findings

A set of four pure states cannot be masked, showing unknown pure states cannot be universally masked.

Constructed a masker $S^lat$ with its maximal maskable set, confirming a previous conjecture.

A commuting subset of mixed states can be masked by an isometry, but not all mixed states.

Abstract

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker $S^\sharp$ and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry $S^{\diamond}$ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries ${S^{\sharp}}$ and ${S^{\diamond}}$, respectively.