Hiding and masking quantum information in complex and real quantum mechanics

TL;DR

This paper explores the fundamental limits of hiding and masking quantum information, demonstrating that while certain real quantum states can be fully hidden in correlations, the set of maskable states is maximal and connected to entanglement.

Contribution

It extends no-hiding and no-masking theorems to informationally complete states and reveals how real quantum states can be completely masked using Clifford algebra representations.

Findings

Informationally complete states cannot be hidden or masked.

Real quantum states can be fully hidden in correlations with exponential Hilbert space growth.

The set of real quantum states is maximally maskable and linked to maximally entangled states.

Abstract

Classical information can be completely hidden in the correlations of bipartite quantum systems. However, it is impossible to hide or mask all quantum information according to the no-hiding and no-masking theorems derived recently. Here we show that any set of informationally complete quantum states is neither hidable nor maskable, thereby strengthening the no-hiding and no-masking theorems known before. Then, by virtue of Hurwitz-Radon matrices (representations of the Clifford algebra), we show that information about real quantum states can be completely hidden in the correlations, although the minimum dimension of the composite Hilbert space required increases exponentially with the dimension of the original Hilbert space. Moreover, the set of real quantum states is a maximal maskable set within quantum theory and has a surprising connection with maximally entangled states. These results offer valuable insight on the potential and limit of hiding and masking quantum information, which are of intrinsic interest to a number of active research areas.