Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Local-available quantum correlation swapping in one-parameter X states

Hermann L. Albrecht

TL;DR

The paper investigates the redistribution of local-available quantum correlations (LAQC) via quantum correlation swapping (QCS) in pairs of 2-qubit X states. It derives a general AD-state form after a projective measurement on the middle qubits and establishes conditions under which the swapped state retains nonzero LAQC, highlighting the role of initial coherence parameters. By examining five one-parameter X-state families (Werner, α-, β-, ρ_v, MEMS), it computes LAQC and compares with entanglement, showing LAQC can persist or even dominate when entanglement vanishes, and that in some cases the swapped state is separable yet still holds nonzero LAQC. These results suggest LAQC can serve as a robust resource in quantum information tasks and motivate further exploration of LAQC-based protocols in quantum networks.

Abstract

Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. In 2015, Mundarain and Ladrón de Guevara [Quantum Inf. Process. 14, 4493 (2015)] introduced local-available quantum correlations (LAQC), which are a promising yet understudied quantum correlation. Recently, Bellorin et al. [Int. J. Mod. Phys. B 36, 22500990 (2022), Int. J. Mod. Phys. B 36, 2250154 (2022)] obtained exact analytical results for the LAQC quantifier of general 2-qubit X states. Building up from those results, we analyzed the LAQC swapping for 2-qubit X states. As expected, we find that if the initial states are non-classical and the one used for the projective measurement is entangled, the final state will generally have non-zero LAQC. Using the properties of this quantum correlation, we establish the conditions for a QCS scheme that leads to a final state with a non-zero LAQC measure. We illustrate these results by analyzing five families of one-parameter 2-qubit X states, including families where the projective measure leads to a separable state, but whose LAQC measure is non-zero. This feature opens the possibility for this quantum correlation to be considered a genuine resource in quantum information technology.

Local-available quantum correlation swapping in one-parameter X states

TL;DR

The paper investigates the redistribution of local-available quantum correlations (LAQC) via quantum correlation swapping (QCS) in pairs of 2-qubit X states. It derives a general AD-state form after a projective measurement on the middle qubits and establishes conditions under which the swapped state retains nonzero LAQC, highlighting the role of initial coherence parameters. By examining five one-parameter X-state families (Werner, α-, β-, ρ_v, MEMS), it computes LAQC and compares with entanglement, showing LAQC can persist or even dominate when entanglement vanishes, and that in some cases the swapped state is separable yet still holds nonzero LAQC. These results suggest LAQC can serve as a robust resource in quantum information tasks and motivate further exploration of LAQC-based protocols in quantum networks.

Abstract

Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. In 2015, Mundarain and Ladrón de Guevara [Quantum Inf. Process. 14, 4493 (2015)] introduced local-available quantum correlations (LAQC), which are a promising yet understudied quantum correlation. Recently, Bellorin et al. [Int. J. Mod. Phys. B 36, 22500990 (2022), Int. J. Mod. Phys. B 36, 2250154 (2022)] obtained exact analytical results for the LAQC quantifier of general 2-qubit X states. Building up from those results, we analyzed the LAQC swapping for 2-qubit X states. As expected, we find that if the initial states are non-classical and the one used for the projective measurement is entangled, the final state will generally have non-zero LAQC. Using the properties of this quantum correlation, we establish the conditions for a QCS scheme that leads to a final state with a non-zero LAQC measure. We illustrate these results by analyzing five families of one-parameter 2-qubit X states, including families where the projective measure leads to a separable state, but whose LAQC measure is non-zero. This feature opens the possibility for this quantum correlation to be considered a genuine resource in quantum information technology.

Paper Structure

This paper contains 10 sections, 2 theorems, 66 equations, 11 figures.

Table of Contents

  1. One-parameter 2-qubit X states
  2. Local-available quantum correlations of 2-qubit X states
  3. Application to specific one-parameter X-states
  4. LAQC swapping in 2-qubit X states
  5. Werner states
  6. $\alpha$-states
  7. $\beta$-states
  8. One-Parameter Mixed States involving a basis element
  9. Maximally Entangled Mixed States
  10. Summary and Conclusions

Key Result

Theorem 1

The resulting state $\rho_X^{AD}$ of a quantum correlation swapping protocol has non-null LAQC if the initial $\rho_X^{AB}$ and $\rho_X^{CD}$ have non-null $T_1$ and $T_2$ parameters.

Figures (11)

  • Figure 1: Schematic representation of quantum correlation swapping via a projective measurement using a pure state $\ket{\psi}$.
  • Figure 2: Concurrence (dashed) and LAQC (solid) for Werner states \ref{['eq:rho-Werner-Psi-']}.
  • Figure 3: Concurrence (dashed) and LAQC (solid) for $\alpha$-states \ref{['eq:X-states-alpha']}.
  • Figure 4: Concurrence (dashed) and LAQC (solid) for $\beta$-states \ref{['eq:X-states-beta']}.
  • Figure 5: Concurrence (dashed) and LAQC (solid) for $\rho_v$\ref{['eq:rho-VV-general']}.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof