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arXiv:2605.29717

Discrete and Continuous Wigner Functions in Open Quantum Systems: Non-Markovian and Thermodynamic Effects

Jai Lalita

quant-phSubmitted May 28, 2026• Announced May 29, 2026• 0 citations
arXivHTMLPDF

Abstract

The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)

Comments
Ph.D. thesis, Indian Institute of Technology Jodhpur (2026)

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•Oct 1, 2026•0 citations
The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)
Abstract The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. The idea of WM and QMR has recently been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocols. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions with(without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping and random telegraph noise quantum channels. To benchmark the performance of negative quantum states, we calculate their success probability. We compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.
Abstract The negativity of the discrete Wigner functions (DWFs) is a measure of non‐classicality and is often used to quantify the degree of quantum coherence in a system. The study of Wigner negativity and its evolution under different quantum channels can provide insight into the stability and robustness of quantum states under their interaction with the environment, which is essential for developing practical quantum computing systems. The variation of DWF negativity of qubit, qutrit, and two‐qubit systems under the action of (non)‐Markovian random telegraph noise (RTN) and amplitude damping (AD) quantum channels is investigated. Different negative quantum states that can be used as a resource for quantum computation and quantum teleportation are constructed. The success of quantum computation and teleportation is estimated for these states under (non)‐Markovian evolutions.
This study explores robust entangled states described using the framework of discrete Wigner functions. Notably, these states are known to outperform the Bell state in measures of entanglement in the presence of non-Markovian noise. Our study focuses on methods for preparing these states using quantum circuits that can be implemented on superconducting hardware and testing the efficacy of these methods on IBM's quantum device. We present quantum circuits for state preparation and validate them through tomographic reconstruction on the IBM \emph{ibm\_brisbane} device. We propose a teleportation scheme that leverages these entangled states as a resource. We believe that these entangled states have the potential to be used in place of the traditional Bell state in scenarios where non-Markovian errors are prevalent.
We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.
We investigate the dynamics of non-classical correlations and quantum coherence in open quantum systems by employing metrics like local quantum Fisher information, local quantum uncertainty, and quantum Jensen-Shannon divergence. Our focus here is on a system of two qubits in two distinct physical situations: the first one when the two qubits are coupled to a single-mode cavity, while the second consists of two qubits immersed in dephasing reservoirs. Our study places significant emphasis on how the evolution of these quantum criterion is influenced by the initial state's purity (whether pure or mixed) and the nature of the environment (whether Markovian or non-Markovian). We observe that a decrease in the initial state's purity corresponds to a reduction in both quantum correlations and quantum coherence, whereas higher purity enhances these quantumness. Furthermore, we establish a quantum teleportation strategy based on the two different physical scenarios. In this approach, the resulting state of the two qubits functions as a quantum channel integrated into a quantum teleportation protocol. We also analyze how the purity of the initial state and the Markovian or non-Markovian regimes impact the quantum teleportation process.
The generation of non-Gaussian states of bosonic systems described by continuous quantum degrees of freedom is of interest in a variety of contexts, ranging from quantum foundations to computation and communication. A crucial feature of genuine non-Gaussian states is that they cannot be described in general with a non-negative Wignerquasi-probability distribution. In particular, this feature is equivalent to contextuality and it underpins all attempts at attaining quantum computational advantage in a universal setting. In this thesis, the generation of Wigner-negative states is addressed, pursuing two approaches. First, in an optomechanical-like setting, we develop schemes to generate Wigner-negative states of two massive mechanical systems, in turn correlated such that they also feature entanglement, another genuine quantum hallmark. These schemes are based on driven-dissipative systems where dissipation is properly engineered by taking advantage of linear-and-quadratic optomechanical interactions. We address the robustness of these schemes when uncontrollable noisy channels are included in the dynamics, proving that their resilience is comparable to Gaussian schemes that have already been implemented experimentally. Second, considering in particular circuit QED systems and trapped ions, we propose a method to engineer a set of Hamiltonian evolutions that are universal in terms of single-mode state preparation. This method is based on a driven quantum Rabi model, where the desired evolution is effectively imprinted on a continuous-variable degree of freedom by its interaction with a properly driven two-level system. We demonstrate the universality of such approach by simulating the generation of multi-squeezed and other states, including the celebrated cubic-phase state. We also consider the effect of noise in realistic settings, showing in particular that in systems involving superconducting qubits, the generation of tri-squeezed states --- a universal resource for continuous-variable quantum computation which we prove to display larger Wigner negativities with respect to Fock and cubic-phase states for the same energy --- is within experimental reach.