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arXiv:0710.2238

Disentanglement in qubit-qutrit systems

Mazhar Ali, A. R. P. Rau, Kedar S. Ranade

Published Oct 11, 2007• 3 citations
arXivHTMLPDF

Abstract

We examine the phenomenon of {\it entanglement sudden death} (ESD) for $(2 \times 3)$-dimensional systems. As for $2 \times 2$ systems, the negativity vanishes in finite time for some entangled pure as well as mixed states. While locally equivalent pure states do so asymptotically. Interference between the decay of the two upper levels to the lowest one in the qutrit adds further richness to ESD in this systems.

DOI
10.48550/arxiv.0710.2238

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We examine the phenomenon of {\it entanglement sudden death} (ESD) for (2×3)(2 \times 3)(2×3)-dimensional systems. As for 2×22 \times 22×2 systems, the negativity vanishes in finite time for some entangled pure as well as mixed states. While locally equivalent pure states do so asymptotically. Interference between the decay of the two upper levels to the lowest one in the qutrit adds further richness to ESD in this systems.
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.
Decoherence and disentanglement are phenomena central to quantum mechanics. Here, we consider the relative rates of decoherence and disentanglement in two‐qubit, three‐qubit, and two‐qutrit systems when subject to pure dephasing noise alone, and a very recent result for d×d systems. Of particular interest is the specific counterintuitive effect related to the nonadditivity of such weak noises, known as Entanglement Sudden Death (ESD), in which the entanglement of a composite quantum system goes abruptly to zero in finite time, coherence only exponentially decaying. We discuss these results in the context of the foundations of quantum mechanics.
In this work, we consider non-interacting atomic two level and three level (qubit-qutrit) systems interacting with a common environment in vacuum state. The interaction with the environment leads to the decoherece of the system due to spontaneous emission of atomic excited states which results in the decay of entanglement and other correlations of the qubit-qutrit system. We study the dynamics of entanglement for different initial class of states and negativity is used as a measure to quantify the degree of entanglement of qubit-qutrit system, the three level systems are considered in V configuration. We construct a class of rank dependant mixed boundary qubit-qutrit states as initial states. We observe entanglement sudden death for higher rank mixed boundary qubit-qutrit states.
This thesis is a theoretical study of entanglement dynamics and its control of qubit-qubit and qubit-qutrit systems. In particular, we focus on the decay of entanglement of quantum states interacting with dissipative environments. Qubit-qubit entanglement may vanish suddenly while interacting with statistically independent vacuum reservoirs. Such finite-time disentanglement is called sudden death of entanglement(ESD). We investigate entanglement sudden death of qubit-qubit and qubit-qutrit systems interacting with statistically independent reservoirs at zero- and finite-temperature. It is shown that for zero-temperature reservoirs, some entangled states exhibit sudden death while others lose their entanglement only after infinite time. Thus, there are two possible routes of entanglement decay, namely sudden death and asymptotic decay. We demonstrate that starting with an initial condition which leads to finite-time disentanglement, we can alter the future course of entanglement by local unitary actions. In other words, it is possible to put the quantum states on other track of decay once they are on a particular route of decay. We show that one can accelerate or delay sudden death. However, there is a critical time such that if local actions are taken before that critical time then sudden death can be delayed to infinity. Any local unitary action taken after that critical time can only accelerate or delay sudden death. In finite-temparature reservoirs, we demonstrate that a whole class of entangled states exhibit sudden death. This conclusion is valid if at least one of the reservoirs is at finite-temperature. However, we show that we can still hasten or delay sudden death by local unitary transformations up to some finite time. We also study sudden death for qubit-qutrit systems. Similar to qubit-qubit systems, some states exhibit sudden death while others do not. However, the process of disentanglement can be effected due to existence of quantum interference between excited levels of qutrit. We show that it is possible to hasten, delay, or avoid sudden death by local unitary actions taken later in time.
The unavoidable and irreversible interaction between an entangled quantum system and its environment causes decoherence of the individual qubits as well as degradation of the entanglement between them. Entanglement sudden death (ESD) is the phenomenon wherein disentanglement happens in finite time even when individual qubits decohere only asymptotically in time due to noise. Prolonging the entanglement is essential for the practical realization of entanglement-based quantum information and computation protocols. For this purpose, the local NOT operation in the computational basis on one or both qubits has been proposed. Here, we formulate an all-optical experimental setup involving such NOT operations that can hasten, delay, or completely avert ESD, all depending on when it is applied during the process of decoherence. Analytical expressions for these are derived in terms of parameters of the initial state’s density matrix, whether for pure or mixed entangled states. After a discussion of the schematics of the experiment, the problem is theoretically analyzed, and simulation results of such manipulations of ESD are presented.
We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death (ESD) is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the case with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.