[Paper Review] Wigner function of noisy accelerated two-qubit system

M. Y. Abd‐Rabbou, N. Metwally+2 more|arXiv (Cornell University)|Mar 22, 2019

Quantum Information and Cryptography24 references4 citations

TL;DR

This paper investigates the Wigner function of a two-qubit system under acceleration and various noisy channels, using it as a probe for quantum and classical correlations. It shows that acceleration and noise degrade quantum correlations, but distribution angles can suppress decoherence; phase flip and bit-phase flip channels preserve quantum correlations over broad parameter ranges, while bit flip channels cause rapid loss of entanglement, with Wigner function profiles revealing distinct classical (hemisphere) and quantum (lune/cap) correlation structures.

ABSTRACT

In this manuscript, the behavior of the Wigner function of accelerated and non-accelerated two qubit system passing through different noisy channels is discussed. The decoherence of the initial quantum correlation due to the noisy channels and the acceleration process is investigated by means of Wigner function. The negative (positive) behavior of the Wigner function predicts the gain of the quantum (classical) correlations. Based on the upper and lower bounds of the Wigner function, the entangled initial state loses its quantum correlation due the acceleration process and the strengths of the noisy channels. However, by controlling the distribution angles, the decoherence of these quantum correlation may be suppressed. For accelerated state, the robustness of the quantum correlations contained in the initial state appears in different ranges of the distribution angles depending on the noisy type. For the bit phase flip and the phase flip channels, the robustness of the quantum correlations is shown at any acceleration and large range of distribution angles. However, the fragility of the quantum correlation is depicted for large values for strength of the bit flip channel. Different profiles of the Wigner function are exhibited for the quantum and classical correlations, cup, lune, hemisphere.

Motivation & Objective

• To study the behavior of the Wigner function in accelerated two-qubit systems under noisy environments.
• To investigate how acceleration and noisy channels affect quantum and classical correlations using the Wigner function as a diagnostic tool.
• To determine the robustness of quantum correlations against decoherence induced by different noise types and acceleration.
• To explore the role of distribution angles as control parameters to suppress decoherence in noisy and accelerated quantum systems.

Proposed method

• The Wigner function is constructed using the SU(2) algebraic formalism, with r-parameterized quasi-probability distributions for s = 0 (Wigner function).
• The initial two-qubit state is prepared as an X-state in the computational basis, with density matrix expressed in terms of coefficients ϱ₁₁, ϱ₂₂, and ϱ₃₃.
• Noise channels—amplitude damping, bit flip, bit-phase flip, phase flip—are modeled using Kraus operators, and their effects are applied to the density matrix to simulate decoherence.
• The Wigner function is computed on the Bloch sphere surface using angular coordinates (θ, φ), with r representing the acceleration parameter.
• The negativity of the Wigner function is used as a signature of quantum correlation, while positivity indicates classical correlation.
• Numerical simulations and 3D plots of W(r, θ) are used to visualize the evolution of quantum and classical correlations across parameter space.

Experimental results

Research questions

• RQ1 How does acceleration affect the Wigner function and the resulting quantum correlations in a two-qubit system?
• RQ2 How do different noisy channels (amplitude damping, bit flip, bit-phase flip, phase flip) alter the Wigner function and the balance between quantum and classical correlations?
• RQ3 Can the distribution angles θ and φ be used as control parameters to suppress decoherence in accelerated and noisy two-qubit systems?
• RQ4 What are the distinct geometric profiles (cap, lune, hemisphere) of the Wigner function, and how do they relate to classical and quantum correlation regions?
• RQ5 How do the upper and lower bounds of the Wigner function vary with channel strength and acceleration parameter?

Key findings

• The Wigner function becomes positive (indicating classical correlation) when the initial entangled state undergoes decoherence due to acceleration or noise, with negativity signaling preserved quantum correlation.
• For the phase flip and bit-phase flip channels, quantum correlations remain robust across a wide range of acceleration and distribution angles, particularly at large θ.
• The bit flip channel causes rapid degradation of quantum correlations, with the Wigner function showing minimal negativity at high channel strengths (e.g., pbf = 0.8) and θ > 3π/4.
• At large acceleration (r > 0.5) and θ > π/2, the system becomes separable regardless of channel type, indicating loss of entanglement.
• The amplitude damping channel preserves quantum correlation at small p and large θ, or at large p and small θ, showing dual robustness depending on parameter regime.
• The Wigner function profiles evolve into distinct geometric shapes: quantum correlations appear as a lune or cap, while classical correlations manifest as upper or lower hemispheres, especially under phase flip noise as p_pf increases.