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A Novel State-Space Diagram Analysis for Entanglement Transitions Using Time-Dependent Separability Measures

Kavin Murugesan, Aayush Chebolu, Christian Polilen

Published Oct 17, 2025• 0 citations
Publisher

Abstract

This paper will analyze the impact of “stochastic noises” on open quantum systems, also known as systems exposed to their environment. In the real world, entangled systems are often subject to stochastic environmental noises that result in decoherence and corruption of their quantum properties. This poses a significant challenge for the implementation of quantum entanglement in fields such as quantum computing and quantum informatics. We will describe the dynamics and evolution of these entangled systems as they decay from a maximally entangled state to a separated state. These dynamics can be highly sensitive to the type and strength of noise, leading to a wide variety of decay behaviors. A special phenomenon we encounter is Entanglement Sudden Death (ESD), where entanglement dies inexplicably within a short period of time. We will also analyze the time-dependent distance from the separability boundary, denoted Λ, within these evolving systems.

DOI
10.33774/coe-2025-93597

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This paper will analyze the impact of “stochastic noises” on open quantum systems, also known as systems exposed to their environment. In the real world, entangled systems are often subject to stochastic environmental noises that result in decoherence and corruption of their quantum properties. This poses a significant challenge for the implementation of quantum entanglement in fields such as quantum computing and quantum informatics. We will describe the dynamics and evolution of these entangled systems as they decay from a maximally entangled state to a separated state. These dynamics can be highly sensitive to the type and strength of noise, leading to a wide variety of decay behaviors. A special phenomenon we encounter is Entanglement Sudden Death (ESD), where entanglement dies inexplicably within a short period of time. We will also analyze the time-dependent distance from the separability boundary, denoted Λ, within these evolving systems.
In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.
Quantum entanglement manifests as a distinctive correlation between particles that transcends classical boundaries when their quantum states cannot be described independently. On the other hand, as quantum systems interact with their surroundings, decoherence emerges, leading to the gradual decay of quantum coherence and entanglement. In the case of entanglement, this is known as entanglement sudden death (ESD). Decoherence mechanisms are examined, focusing on how various environmental factors, such as thermal, electromagnetic, and collisional decoherence, influence the integrity of entangled states. The role of quantum noise, such as amplitude damping, phase damping, and depolarizing, is also analyzed. By integrating theoretical insights with experimental findings, this study highlights the delicate balance between maintaining entanglement and mitigating decoherence. The findings have significant implications for the development of quantum technologies, including quantum computing and quantum communication, where preserving entanglement is crucial for achieving robust and reliable performance.
Strangeness of quantum physical laws is very fascinating aspect for all of us. In various composite quantum systems it was found that the finite time disentanglement called Entanglement sudden death takes place.Entangalment sudden death is a very well known phenomena in which qubits die after in a particular time. In our case we have studied two qubit quantum system as maximally entangled systems. We can expand it for many qubit systems also. We examine the behaviour of these systems under amplitude damping noise. The other environmental noises such as phase damping and depolarisation were also studied. All these noises were applied on single qubit as well as on both the qubits. Class of X-states has been used for the study.
We address the dynamics of entanglement and quantum discord for two noninteracting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e., coupled with an external environment characterized by a noise spectrum of the form $1/{f}^{\ensuremath{\alpha}}$. More specifically, we address systems in which the Gaussian approximation fails, i.e., mere knowledge of the spectrum is not enough to determine the dynamics of quantum correlations. We thus investigate the dynamics for two different configurations of the environment: in the first case, the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with fixed switching rates. In both cases, we found analytical expressions for the time dependence of entanglement and quantum discord, which may also be extended to a collection of fluctuators with random switching rates. The environmental noise is introduced by means of stochastic time-dependent terms in the Hamiltonian, and this allows us to describe the effects of both separate and common environments. We show that the non-Gaussian character of the noise may lead to significant effects, e.g., environments with the same power spectrum, but different configurations give rise to the opposite behavior for quantum correlations. In particular, depending on the characteristics of the environmental noise considered, both entanglement and discord display either a monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure of the environment, in addition to its noise spectrum, is relevant for the dynamics of quantum correlations and may be a valid starting point for the engineering of non-Gaussian colored environments.
Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment [1, 2, 3]. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or "realization") corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the "Fifth International Workshop DICE2010" by the first author and have been the subject of a prior publication [4].