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arXiv:2210.01854

Unexpected Robustness of Multipartite Entanglement against Sudden Death from Spontaneous Emission

Songbo Xie, Daniel Younis, Joseph H. Eberly

Published Oct 4, 2022• 0 citations
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Abstract

Entanglement is known to decay even in isolated systems, an effect attributed to spontaneous emission. This fragility of entanglement can be exacerbated by entanglement sudden death (ESD), where entanglement drops to zero abruptly within a finite time. It is natural to assume that multipartite entanglement is more vulnerable to ESD, as it involves more parties experiencing spontaneous emission. In this work, we challenge this assumption and present a contrasting conclusion, asserting that multipartite entanglement demonstrates increased robustness against ESD from spontaneous emission.

DOI
10.48550/arxiv.2210.01854

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Entanglement is known to decay even in isolated systems, an effect attributed to spontaneous emission. This fragility of entanglement can be exacerbated by entanglement sudden death (ESD), where entanglement drops to zero abruptly within a finite time. It is natural to assume that multipartite entanglement is more vulnerable to ESD, as it involves more parties experiencing spontaneous emission. In this work, we challenge this assumption and present a contrasting conclusion, asserting that multipartite entanglement demonstrates increased robustness against ESD from spontaneous emission.
The effect of entanglement sudden death (ESD) can arise when entangling interactions convert purely bipartite entangled states into more generally entangled states. As a result, ESD can also be seen as a function of partitioning of the system, not just of time, as the system partitioning defines different (multipartite) entanglement classes. Computing both geometric entanglement hierarchies and the generalization of concurrence allows one to demonstrate that different methods of analysing quantum correlations provide both qualitative and quantitatively different descriptions of two commonly cited examples of ESD. These results follow directly from the inequivalence of entanglement and quantum correlations, the latter of which can exist in a state without the former.
Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.
Decoherence, often caused by unavoidable coupling with the environment, leads to degradation of quantum coherence. For a multipartite quantum system, decoherence leads to degradation of entanglement and, in certain cases, entanglement sudden death. Tackling decoherence, thus, is a critical issue faced in quantum information, as entanglement is a vital resource for many quantum information applications including quantum computing, quantum cryptography, quantum teleportation, and quantum metrology. Here, we propose and demonstrate a novel scheme to protect entanglement from decoherence. Our entanglement protection scheme makes use of the quantum measurement itself for actively battling against decoherence and it can effectively circumvent even entanglement sudden death (ESD).
Dissipation may cause two initially entangled qubits to evolve into a separable state in a finite time. This behavior is called entanglement sudden death (ESD). We study to what extent quantum error correction can combat ESD. We find that in some cases quantum error correction can delay entanglement sudden death but in other cases quantum error correction may cause ESD for states that otherwise do not suffer from it. Our analysis also shows that fidelity may not be the best measure to compare the efficiency of different error correction codes since the fidelity is not directly coupled to a state's remaining entanglement.