Robustness of quantum data hiding against entangled catalysts and memory

TL;DR

This paper explores the robustness of quantum data hiding against advanced quantum resources, showing that separable hiding states remain secure while entangled states can be distinguished with quantum memory.

Contribution

It introduces a unified framework for state discrimination with catalysts and memory, proving separable states are robust against such resources and highlighting the vulnerability of some entangled states.

Findings

Separable states are robust against catalysts and memory.

Quantum memory can nearly perfectly discriminate some entangled states.

The framework unifies catalytic and memory-assisted discrimination protocols.

Abstract

Quantum data hiding stores classical information in bipartite quantum states that are, in principle, perfectly distinguishable, yet remain almost indistinguishable without access to a quantum communication channel. Here, we investigate whether this limitation can be overcome when the communicating parties are assisted by additional quantum resources. We develop a general framework for state discrimination that unifies catalytic and memory-assisted local discrimination protocols and analyze their power to reveal hidden information. We prove that when the hiding states are separable, neither entangled catalysts nor quantum memory can increase the optimal discrimination probability, establishing the robustness of separable data-hiding schemes. In contrast, for some entangled states, a reusable quantum memory turns locally indistinguishable states into ones that can be discriminated almost perfectly. Our results delineate the fundamental limits of catalytic and memory-assisted state discrimination and identify separable encodings as a robust strategy for quantum data hiding.