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Quantifying entanglement in multipartite conditional states of open\n quantum systems by measurements of their photonic environment

Juan Diego Urbina, Walter T. Strunz, Carlos Viviescas

Published Jan 26, 2012• 0 citations
OpenAlex

Abstract

A key lesson of the decoherence program is that information flowing out from\nan open system is stored in the quantum state of the surroundings.\nSimultaneously, quantum measurement theory shows that the evolution of any open\nsystem when its environment is measured is nonlinear and leads to pure states\nconditioned on the measurement record. Here we report the discovery of a\nfundamental relation between measurement and entanglement which is\ncharacteristic of this scenario. It takes the form of a scaling law between the\namount of entanglement in the conditional state of the system and the\nprobabilities of the experimental outcomes obtained from measuring the state of\nthe environment. Using the scaling, we construct the distribution of\nentanglement over the ensemble of experimental outcomes for standard models\nwith one open channel and provide rigorous results on finite-time\ndisentanglement in systems coupled to non-Markovian baths. The scaling allows\nthe direct experimental detection and quantification of entanglement in\nconditional states of a large class of open systems by quantum tomography of\nthe bath.

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A key lesson of the decoherence program is that information flowing out from\nan open system is stored in the quantum state of the surroundings.\nSimultaneously, quantum measurement theory shows that the evolution of any open\nsystem when its environment is measured is nonlinear and leads to pure states\nconditioned on the measurement record. Here we report the discovery of a\nfundamental relation between measurement and entanglement which is\ncharacteristic of this scenario. It takes the form of a scaling law between the\namount of entanglement in the conditional state of the system and the\nprobabilities of the experimental outcomes obtained from measuring the state of\nthe environment. Using the scaling, we construct the distribution of\nentanglement over the ensemble of experimental outcomes for standard models\nwith one open channel and provide rigorous results on finite-time\ndisentanglement in systems coupled to non-Markovian baths. The scaling allows\nthe direct experimental detection and quantification of entanglement in\nconditional states of a large class of open systems by quantum tomography of\nthe bath.
A key lesson of the decoherence program is that information flowing out from an open system is stored in the quantum state of the surroundings. Simultaneously, quantum measurement theory shows that the evolution of any open system when its environment is measured is nonlinear and leads to pure states conditioned on the measurement record. Here we report the discovery of a fundamental relation between measurement and entanglement which is characteristic of this scenario. It takes the form of a scaling law between the amount of entanglement in the conditional state of the system and the probabilities of the experimental outcomes obtained from measuring the state of the environment. Using the scaling, we construct the distribution of entanglement over the ensemble of experimental outcomes for standard models with one open channel and provide rigorous results on finite-time disentanglement in systems coupled to non-Markovian baths. The scaling allows the direct experimental detection and quantification of entanglement in conditional states of a large class of open systems by quantum tomography of the bath.
A key lesson of the decoherence program is that information flowing out from an open system is stored in the quantum state of the surroundings. Simultaneously, quantum measurement theory shows that the evolution of any open system when its environment is measured is nonlinear and leads to pure states conditioned on the measurement record. Here we report the discovery of a fundamental relation between measurement and entanglement which is characteristic of this scenario. It takes the form of a scaling law between the amount of entanglement in the conditional state of the system and the probabilities of the experimental outcomes obtained from measuring the state of the environment, with the latter modeled as a bosonic field linearly coupled with the system. Using the scaling, we construct the distribution of entanglement over the ensemble of experimental outcomes for standard models with one open channel and provide rigorous results on finite-time disentanglement in systems coupled to non-Markovian baths. In principle, the scaling allows the direct experimental detection and quantification of entanglement in conditional states of a large class of open systems by quantum tomography of the bath even when it consists of a single mode.
We investigate the distribution of entanglement in tripartite quantum systems under the influence of noisy environment. Entanglement distribution is an important concept to understand the robustness of entanglement in multipartite systems, while preserving multipartite entanglement amid decoherence remains a major challenge. Measuring multipartite entanglement in mixed states under decoherence is challenging. We quantify tripartite entanglement using relative entropy due to its applicability to both pure and mixed states. In this work, we explore how entanglement is distributed among the qubits of multipartite states when the three qubits are exposed to multipartite dephasing setting. In our study we use various pure and mixed tripartite states subjected to both Markovian and non-Markovian Local/Common bosonic reservoir at finite temperature. We show that the robustness of tripartite systems to decoherence depends on the distribution of entanglement and its interaction with various configurations and parameters of the bath.
Decoherence is an unavoidable effect of the quantum system coupled to an environment, which leads to the system evolving from a pure state to a mixed one. A critical issue here is that the reduction of purity is quantum or classical, which corresponds to whether or not entanglement is generated between the system and environment. We report a proof-of-principle experimental investigation of such entanglement in a simple but paradigmatic case, in which a qubit system interacts with a pure dephasing channel. The pure dephasing process is realized in a linear photonic system, and the experiment is a validation in a very controlled setting. By adopting previous methods to detect qubit-environment entanglement, we prove that such entanglement can be detected by performing local measurements on only one subsystem, even when the other subsystem in the pair cannot be detected. Our experiment paves the way for investigating features of open quantum system dynamics.
Experimentally quantifying entanglement and coherence is extremely important in quantum information processing. In a multipartite quantum system, usually the fidelity of the system's state compared to a target state is measured to detect its entanglement. The authors present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuine multipartite entanglement and coherence, allowing quick quantification of system states without quantum state tomography in experiments. The method works generally, for several entanglement measures and coherence measures, and examples of real experimental states are analyzed in detail.
Abstract Protecting entanglement from decoherence is a critical aspect of quantum information processsing. For many-body quantum systems evolving under decoherence, estimating multipartite entanglement is challenging. This challenge can be met up by considering a distance-based measure such as relative entropy of entanglement which decisively measures entanglement in both pure as well as mixed states. In this work, we investigate the tripartite entanglement dynamics of pure and mixed states in the presence of a structured dephasing environment at finite temperature. We show that the robustness of the quantum system to decoherence is dependent on the distribution of entanglement and its relation to different configurations of the bath. If the bath is structured individually such that each qubit has its own environment, the system has different dynamics compared to when the bath is common to all the three qubits. From the results we conjecture that there is a connection between the distribution of entanglement among the qubits and the distribution of bath degrees of freedom, and the interplay of these two distributions determines the decay rate of the entanglement dynamics. The sustainability of tripartite entanglement is shown to be enhanced significantly in the presence of reservoir memory.