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Frontiers in Optics

Sudden Death at High NOON

Asma Al-Qasimi, Daniel F. V. James

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Entanglement Sudden Death (ESD) is the disappearance of entanglement in finite time. We show that in Continuous Variable Quantum Systems (CVQS), NOON states and other two-mode N-photon states, dephasing induced ESD does not occur.
DOI
10.1364/fio.2008.ftuq6

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We study the dynamics of entanglement in continuous variable quantum systems. Specifically, we study the phenomena of entanglement sudden death (ESD) in general two-mode-N-photon states undergoing pure dephasing. We show that for these circumstances, ESD never occurs. These states are generalizations of the so-called high NOON states (i.e., a superposition of N photons in the first mode, O in the second, with O photons in the first, N in the second), shown to decrease the Rayleigh limit of lambda to lambda/N, which promises great improvement in resolution of interference patterns if states with large N are physically realized [Phys. Rev. Lett.85, 2733 (2000)]. However, we show that in dephasing NOON states, the time to reach some critical visibility Vcrit, scales inversely with N2. On the practical level, this shows that as N increases, the visibility degrades much faster, which is likely to be a considerable drawback for any practical application of these states.
Entanglement sudden death (ESD), the complete loss of entanglement in finite time, is demonstrated to occur in a class of bipartite states of qudit pairs of any finite dimension d>2d>2d>2, when prepared in so-called ``isotropic states'' and subject to multilocal dephasing noise alone. This extends previous results for qubit pairs [T. Yu and J. H. Eberly, Phys. Rev. Lett. 97, 140403 (2006)] to all qudit pairs with d>2d>2d>2.
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.
Abstract We investigate the entanglement dynamics in a 2 ⨂ 3 quantum system consisting of a two-level atom and a three-level V-type atom interacting independently with their environments. Pure and mixed initial states, including one-parameter and two-parameter states of the atoms are analyzed. It is observed that the entanglement in the qubit-qutrit system disappears in a finite time, commonly referred to as ESD (entanglement sudden death). We analytically calculate the ESD time using the negativity as an entanglement measure. Remarkably, the presence of vacuum-induced coherence in the three-level atom (qutrit) delays the occurrence of ESD and effectively protects the entanglement from decoherence.
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.
Decoherence due to the unwanted interaction between a quantum system and environment leads to the degradation of quantum coherence. In particular, for an entangled state, decoherence makes a loss of entanglement and Bell nonlocality known as entanglement sudden death (ESD), and Bell nonlocality sudden death (BNSD). Here, we theoretically investigate the entanglement and Bell nonlocality of a bipartite entangled state under three types of decoherence, amplitude damping, phase damping, and depolarizing. Our result provides the bound of decoherence strength that does not lose the entanglement and Bell nonlocality. In addition, we find two interesting features. One is that the entanglement can survive even though one of the entangled qubits is affected by a large strength of decoherence if the other qubit is affected by a small enough strength of decoherence except for the depolarizing. The second one is that when a specific form of entangled state is under amplitude damping, the Bell nonlocality shows an asymmetric behavior respect to the decoherence strengths on each qubit. Our work provides comprehensive information on ESD and BNSD for the bipartite entangled state which will be useful to implement quantum information processing in the presence of decoherence.