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.
Highlights
Hiding information in correlations is a simple way of realizing secret sharing [1,2], which is a primitive to cryptography and secure multiparty computation
By virtue of Hurwitz-Radon (HR) matrices [27,28,29], we further show that information about real quantum states can be completely hidden in the correlations
II, we review the basic ideas of hiding and masking quantum information and introduce the concepts of masking spectrum, masking purity, entanglement of masking, and maximal maskable sets
Summary
Hiding information in correlations is a simple way of realizing secret sharing [1,2], which is a primitive to cryptography and secure multiparty computation. We show that it is impossible to hide or mask any set of quantum states that is informationally complete (IC), thereby strengthening the no-hiding and no-masking theorems and establishing an information theoretical underpinning of these no-go results This conclusion can serve as the common starting point for deriving and strengthening a number of re-. Our study offers valuable insight on the potential and limit of hiding and masking quantum information It may shed light on a number of active research areas, including quantum secret sharing [3,4,5], information scrambling, black-hole information paradox [6,7,8,9], resource theory of imaginarity [24,25], and foundational studies on quantum mechanics [33,34,35]. Most technical proofs are relegated to the Appendix
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