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Quantum data hiding with two-qubit separable states

Donghoon Ha, Jeong San Kim

TL;DR

This paper studies data hiding in two-party quantum state discrimination and demonstrates a practical scheme using two-qubit separable, orthogonal states. It derives a bound on local discrimination via PPT measurements and introduces a sufficient condition ensuring that a two-party state ensemble yields exponentially vanishing information under LOCC when replicated L times. The authors illustrate the condition with an explicit two-qubit ensemble parameterized by θ, showing the bound holds (4 f0(θ)f1(θ) < 1) for θ in [0, π/3], enabling a one-bit hidden with asymptotic LOCC secrecy and perfect global recoverability. They discuss extensions to multi-bit hiding and open questions about the universality of the method for orthogonal ensembles.

Abstract

We consider the discrimination of two-party quantum states and provide a quantum data-hiding scheme using two-qubit separable states. We first provide a bound on the optimal local discrimination of two-party quantum states, and establish a sufficient condition under which a two-party quantum state ensemble can be used to construct a data-hiding scheme. We illustrate this condition with examples of two-qubit state ensembles consisting of two orthogonal separable states. As our data-hiding scheme can be implemented with separable states of the lowest possible dimension, its practical realization becomes significantly more attainable.

Quantum data hiding with two-qubit separable states

TL;DR

This paper studies data hiding in two-party quantum state discrimination and demonstrates a practical scheme using two-qubit separable, orthogonal states. It derives a bound on local discrimination via PPT measurements and introduces a sufficient condition ensuring that a two-party state ensemble yields exponentially vanishing information under LOCC when replicated L times. The authors illustrate the condition with an explicit two-qubit ensemble parameterized by θ, showing the bound holds (4 f0(θ)f1(θ) < 1) for θ in [0, π/3], enabling a one-bit hidden with asymptotic LOCC secrecy and perfect global recoverability. They discuss extensions to multi-bit hiding and open questions about the universality of the method for orthogonal ensembles.

Abstract

We consider the discrimination of two-party quantum states and provide a quantum data-hiding scheme using two-qubit separable states. We first provide a bound on the optimal local discrimination of two-party quantum states, and establish a sufficient condition under which a two-party quantum state ensemble can be used to construct a data-hiding scheme. We illustrate this condition with examples of two-qubit state ensembles consisting of two orthogonal separable states. As our data-hiding scheme can be implemented with separable states of the lowest possible dimension, its practical realization becomes significantly more attainable.

Paper Structure

This paper contains 7 sections, 5 theorems, 53 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Two-party quantum state discrimination
  4. Two-party quantum data hiding
  5. Quantum data-hiding scheme using two-qubit separable state ensemble
  6. Discussion
  7. PROOF OF LEMMA \ref{['LEM:SCPT']}

Key Result

Proposition 1

For a two-party quantum state ensemble $\mathcal{E}=\{\eta_{0},\rho_{0};\eta_{1},\rho_{1}\}$ satisfying where we have where $\mathop{\mathrm{Tr}}\nolimits|\cdot|$ denotes the trace norm and the minimum is taken over all possible Hermitian operators $H$ with

Figures (1)

  • Figure 1: The behavior of $4f_{0}(\theta)f_{1}(\theta)$ on the interval $0\leqslant\theta\leqslant\frac{\pi}{3}$. The function takes values approximately $0.9998$ and $0.9983$ at $\theta=\pi/6$ and $\theta=\pi/4$, respectively. When $4f_{0}(\theta)f_{1}(\theta)<1$, the two-qubit separable state ensemble $\mathcal{E}$ in Example \ref{['ex:tqbt']} can be used to construct a one-bit hiding scheme.

Theorems & Definitions (11)

  • Definition 1
  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Lemma 1
  • proof : Proof of Theorem \ref{['thm:cppt']}
  • Corollary 1
  • proof
  • Example 1
  • proof : Proof of Inequality \ref{['eq:sefc']}
  • ...and 1 more