Quantum Data Hiding

TL;DR

This work develops quantum data hiding schemes that securely embed classical data into bipartite quantum states under LOCC constraints, exploiting nonlocality without entanglement. It formalizes PPT-based LOCC restrictions, analyzes both single- and multi-bit hiding using mixtures of Bell states and Werner-state representations, and derives tight upper bounds on information obtainable by LOCC measurements. A central contribution is an efficient, low-entanglement preparation of hiding states via Clifford twirl, establishing a practical route to implement data hiding with polynomial resources. The paper further explores separable-state hiding, additive information properties, and a conditionally secure quantum bit commitment protocol, highlighting both theoretical limits and potential experimental realizations. Overall, it quantifies the trade-offs between entanglement, LOCC limitations, and cryptographic applications in quantum data hiding.

Abstract

We expand on our work on Quantum Data Hiding -- hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

Figures (8)

• Figure 1: (a) A bipartite POVM measurement with two outcomes. (b) Applying the bipartite POVM measurement to two halves of two maximally entangled states $|\Psi_{\max}\rangle$ results in a residual state which is proportional to the transpose of the POVM element corresponding to the measurement outcome.
• Figure 2: Equation (\ref{['tightlt2']}) restricts $(p_{0|0},p_{1|1})$ to the above shaded region. The points $B$, $C$, and $D$ are respectively $({2^{-(n-1)} \over 1+2^{-n}},1)$, $({1-2^{-n} \over 1+2^{-n}},0)$, and $({1 \over 2}{2^n + 2 \over 2^n+1},{1 \over 2}{2^n \over 2^n-1})$. The point $D$ is achievable by a LOCC measurement described in Section \ref{['tightb']}. The expression $p_{0|0} + p_{1|1}$ is maximized at $B$.
• Figure 3: For any pair of orthogonal states $\rho_{0,1}$ on ${\cal H}_{2^n} \otimes {\cal H}_{2^n}$, there exists an LOCC POVM with probabilities $p_{0|0}$, $p_{1|1}$ above the curves shown for $n=1$ and $n=2$. The dashed lines are the simpler, weaker bound of Eq. (\ref{['corr']}).
• Figure 4: Contours of constant upper bound on $\log I({\bf B}:Y)$, Eq. (\ref{['ibou']}), while varying $n$ (the vertical axis) and $k$ (the horizontal axis). The bound on $\log I({\bf B}:Y)$ is calculated using the expression for $\Delta$ in Eq. (\ref{['bou']}) with $L_p$ in Eq. (\ref{['ster']}).
• Figure 5: $(p_{0|0}^{(1)}, p_{1|1}^{(1)})$ attainable by PPT-preserving measurements on $\tau_{0,1}$.

Theorems & Definitions (5)

• Theorem 1
• proof : Security
• Theorem 2
• proof
• proof