Sudden death of entanglement at finite temperature

Abstract

In this paper we consider the decay of quantum entanglement, quantified by the concurrence, of a pair of two-level systems each of which is interacting with a reservoir at finite temperature T. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time i.e. "entanglement sudden death" (ESD) occurs. This class includes all states which previously had been found to have long-lived entanglement in zero temperature reservoirs. Our general result is illustrated by an example.In the past few years there has been considerable interest in the properties of entangled quantum systems. Spurred on by the emergence of compelling applications in quantum information processing, useful methods by which the entanglement of quantum systems can be established and characterized have emerged. Perhaps the most impactful to date has been the simple procedure derived by Wootters [1] for quantifying entanglement for an arbitrary mixed state of a pair of two-level systems. This has provided a very useful tool for measurement of experimental quantum states [2] and is today commonly used in assessing the capabilities of emerging quantum technologies. Building on Wootter's work, recently Yu and Eberly [3] investigated the time evolution of entanglement (quantified using the concurrence) of a bipartite qubit system undergoing various modes of decoherence. Remarkably, they found that, even when there is no interaction, (either directly or through a correlated environment), there are certain states whose entanglement decays exponentially with time, while for other closely related states, the entanglement vanishes completly in a finite time. This "entanglement sudden death" (ESD) is an intriguing and potentially very important discovery. Since the first theoretical demonstration of ESD, further investigations of different systems have been made by various groups [4,5,6,7,8,9,10,11,12,13]. Extending Yu and Eberly's model by considering correlated reservoirs and interactions [5,8,10,12,13], it was shown that entanglement may be created by spontaneous emission (something which has been known for some time [17] in a different context). The ESD has also been predicted for more complicated systems using other entanglement measures [15,16], and an attempt to give a geometric interpretation for the phenomena of ESD has also been made [18]. Very recently, experimental studies have also been carried out to demostrate ESD, using carefully engineered interactions between systems and environments: Sudden death has been observed both in photons [14] and in atomic ensembles [19].From the technological point of view, states which exhibit exponential decay of entanglement, and therefore retain some vestige of this all-important correlation for long periods, are of great interest. Thus it is important to identify precisely in what circumstances ESD will occur. In this paper, we consider qubits in finite temperature reservoirs: instead of the energy of the qubits being lost via spontaneous decay to...

Quantum properties and dynamics ofXstates

“…One of the reasons why X states became so popular in the study of the dynamics of quantum correlations is because of the relatively simple form that the concurrence takes for such states. Moreover since in such studies [41][42][43] they stay in the X form for all times, the simple equation (13) is valid throughout their evolution. To study what types of dynamics preserve the shape of X states we employ the very elegant algebraic characterization of X states presented in [44].…”

q-entropies and the entanglement dynamics of two-qubits interacting with an environment

“…The time evolution of two non-interacting qubits, each of them individually evolving according to (8), is then given by a time dependent density matrix whose elements with respect to the computational basis with ρ T i j (t) = ρ T * ji (t). That is, the matrix ρ T (t) is Hermitian.…”

“…It has been shown that in some cases entanglement can completely disappear in finite times. This phenomenon is known as entanglement sudden death (ESD) [7][8][9][10] and has been observed experimentally by Almeida et al [11]. It is of clear relevance to study and understand ESD and related phenomena occurring during the evolution of open quantum systems, because the actual implementation of quantum computation and other quantum information tasks depend on the longevity of entanglement in multiqubits states.…”

“…This decay of entanglement has recently attracted the interest of many researchers [7,8] because it constitutes one of the main obstacles that have to be overcome in order to develop quantum technologies based upon the controlled manipulation of entangled states [3]. It has been shown that in some cases entanglement can completely disappear in finite times.…”

Two-Level Atom at Finite Temperature

“…First, a very general treatment was based on dissipation phenomena in the damped cavity model [11][12][13]. The problem of the influence of the temperature on the induced inter- * e-mail: tomsow@cft.edu.pl actions between qubits via the electromagnetic field and on their entanglement is recently considered in the context of the so-called sudden death of entanglement phenomenon [14][15][16]. Very often this analysis is carried out in the Jaynes-Cummings model [17] in the rotating wave approximation (RWA) [18][19][20][21].…”