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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Altering the decay of quantum entanglement

A. R. P. Rau, Mazhar Ali, G. Alber

Published Mar 6, 2008• 0 citations
Publisher

Abstract

Decoherence of phases and dissipation of amplitudes can lead to loss of entanglement between two systems. In particular, an initially set-up entanglement of two qubits can end after a finite time in "sudden death". We show how local, unitary actions by the individual qubits can change this fate. In particular, the sudden death can even be averted all together.

DOI
10.1117/12.778760

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Decoherence of phases and dissipation of amplitudes can lead to loss of entanglement between two systems. In particular, an initially set-up entanglement of two qubits can end after a finite time in "sudden death". We show how local, unitary actions by the individual qubits can change this fate. In particular, the sudden death can even be averted all together.
The finite time end of entanglement between two decohering qubits can be modified by local, unitary actions performed during the decoherence process. Depending on the time when such action is taken, the end can be speeded up or slowed down, or even averted all together. This phenomenon offers practical applications for the stabilization of entangled quantum states. Details concerning hastening or delaying the finite-time end of entanglement are presented for two qubits which decay spontaneously into statistically independent reservoirs.
The finite time end of entanglement between two decohering qubits can be modified by local, unitary actions performed during the decoherence process. Depending on the time when such action is taken, the end can be speeded up or slowed down, or even averted all together. This phenomenon offers practical applications for the stabilization of entangled quantum states. Details concerning hastening or delaying the finite-time end of entanglement are presented for two qubits which decay spontaneously into statistically independent reservoirs. Copyright © EPLA, 2008.
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 entanglement dynamics of two interacting qubits in a common vacuum environment. The inevitable environment interaction leads to entanglement sudden death (ESD) in a two qubit entangled state system. The entanglement dynamics can be modified by the use of local unitary operations (quantum gates), applied on the system during its evolution. We show that these operations not only delays or avoids the ESD but also advances the entanglement revival with high concurrence value depending on the time of operation. We have analytically found out different time windows for switching with different quantum gates so that the ESD can be completely avoided in the subsequent evolution of the system. Our result offers practical applications in the field of quantum information processing where the entanglement is a necessary resource.