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Quantifying nonclassical correlations relative to local channels

Cong Xu, Tao Li, Ruonan Ren, Ming-Jing Zhao, Shao-Ming Fei

TL;DR

This work introduces the modified Wigner-Yanase-Dyson (MWYD) skew information $T_(\rho,\Phi)$ for a state relative to a quantum channel and defines a corresponding quantum-correlation measure $D^T_(\rho_{AB}|\Phi_A)$. The authors prove key properties including nonnegativity, unitary covariance, convexity, and contractivity, and relate these to an existing measure $D_$ via a concrete example. They analyze correlations relative to three channel classes: von Neumann measurements, unitary channels, and twirling channels, obtaining optimized and closed-form expressions and connecting to coherence measures and geometric discord. The results provide a channel-relative resource quantify for nonclassical correlations with explicit forms for standard channels and a pathway for interpreting non-Hermitian operator contributions through $T_(\rho,\Phi)$.

Abstract

Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and a quantitative measure of quantum correlations. Their basic properties are explored in detail. Through a specific example, we also compare our correlations measure with the existing one. Moreover, the correlations relative to various channels including the von Neumann measurements, the unitary channels and the twirling channels are analyzed.

Quantifying nonclassical correlations relative to local channels

TL;DR

This work introduces the modified Wigner-Yanase-Dyson (MWYD) skew information for a state relative to a quantum channel and defines a corresponding quantum-correlation measure . The authors prove key properties including nonnegativity, unitary covariance, convexity, and contractivity, and relate these to an existing measure via a concrete example. They analyze correlations relative to three channel classes: von Neumann measurements, unitary channels, and twirling channels, obtaining optimized and closed-form expressions and connecting to coherence measures and geometric discord. The results provide a channel-relative resource quantify for nonclassical correlations with explicit forms for standard channels and a pathway for interpreting non-Hermitian operator contributions through .

Abstract

Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and a quantitative measure of quantum correlations. Their basic properties are explored in detail. Through a specific example, we also compare our correlations measure with the existing one. Moreover, the correlations relative to various channels including the von Neumann measurements, the unitary channels and the twirling channels are analyzed.

Paper Structure

This paper contains 12 sections, 5 theorems, 53 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantum correlations in terms of modified Wigner-Yanase-Dyson (MWYD) skew information
  3. APPLICATIONS
  4. Correlations relative to a von Neumann measurement
  5. Correlations relative to a unitary channel
  6. Correlations relative to twirling channel induced by unitary group
  7. Conclusion
  8. APPENDIX
  9. Proof of Theorem 1
  10. Proof of Theorem 2
  11. Proof of Corollaries 1-3
  12. Proof of Theorem 3

Key Result

Theorem 1

The $T_{\alpha}(\rho,\Phi)$ has the following properties: (i) (Non-negativity) $T_{\alpha}(\rho,\Phi)\geq0$ and $T_{\alpha}(\rho,\Phi)=0$ if $\Phi (\rho^{1-\alpha})=\rho^{1-\alpha}$. (ii) (Ancillary independence) where $\rho_{A}$ and $\rho_{B}$ are quantum states of systems $A$ and $B$, $\Phi_{A}$ and $\mathcal{I}_B$ are quantum channel and the identity channel on systems $A$ and $B$, respectivel

Figures (2)

  • Figure 1: $p=\frac{1}{4}$. The dotted red line and solid red line represent the the correlations $D^T_{\alpha}(\rho_{AB}|\Phi_{AD})$ and $D_{\alpha}(\rho_{AB}|\Phi_{AD})$, respectively, with respect to $\alpha$.
  • Figure 2: $\alpha=\frac{3}{4}$. The dotted red line and solid red line represent the correlations $D^T_{3/4}(\rho_{AB}|\Phi_{AD})$ and $D_{3/4}(\rho_{AB}|\Phi_{AD})$, respectively, with respect to the parameter $p$.

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Theorem 1
  • Definition 3
  • Theorem 2
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • proof
  • proof
  • ...and 2 more