Robustness of quantum data hiding against entangled catalysts and memory

TL;DR

This work addresses whether entangled catalysts or reusable quantum memory can defeat quantum data hiding under LOCC. It introduces a unified, rate-based framework for local state discrimination that encompasses catalytic and memory-assisted strategies and connects them to standard figures of merit like $P_{ m LOCC}$ and $P_{ m opt}$. The authors prove a robust no-advantage theorem for separable encodings, showing $R_{\rm c}=R_{\rm m}=P_{\rm LOCC}$ for all separable data-hiding pairs, while demonstrating that memory can dramatically boost discrimination for certain entangled encodings, achieving arbitrarily high success probabilities with a finite memory dimension. Collectively, these results delineate when catalytic or memory-based resources can overcome data hiding and guide robust encoding design, while outlining open questions about catalyst-based attacks and broader robustness criteria beyond separable states.

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.

Figures (1)

• Figure 1: Local state discrimination with entanglement catalysis and quantum memory. In each round, one of two quantum states $\rho_{Z_1}^{AB}$ is sent to Alice and Bob, where $Z_1$ is a random variable taking the values $0$ or $1$ with equal probability. In addition, Alice and Bob share a quantum memory $A'B'$, initialized in the state $\mu_1^{A'B'}$. They attempt to infer the value of $Z_1$ by performing an LOCC protocol on the joint system $\rho_{Z_1}^{AB} \otimes \mu_1^{A'B'}$ and recording their guess as $Y_1 \in \{0,1\}$. In the next round, the updated memory state $\mu_2^{A'B'}$ is reused to guess $Z_2$, and the procedure continues iteratively. In the catalytic setting, the memory state remains unchanged throughout the process, that is, $\mu_1^{A'B'} = \mu_2^{A'B'} = \mu_j^{A'B'}$ for all rounds $j$. The figure shows the first two rounds of the process.

Theorems & Definitions (6)

• Theorem 1
• Theorem 2
• Proposition 1
• proof
• Proposition 2
• proof