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Advances in Optics and Photonics

Coherence and entanglement in a two-qubit system

Miguel Orszag, Maritza Hernandez

Published Mar 17, 2010• 36 citations
Publisher

Abstract

Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.

DOI
10.1364/aop.2.000229

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We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.

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Role of initial coherence on entanglement dynamics of two qubit X states

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Abstract Bipartite entanglement is a necessary resource in most processes in quantum information science. Decoherence resulting from the interaction of the bipartite system with environment not only degrades the entanglement, but can result in abrupt disentanglement, known as entanglement sudden death (ESD). In some cases, a subsequent revival of entanglement is also possible. ESD is an undesirable feature for the state to be used as a resource in applications. In order to delay or avoid ESD, it is necessary to understand its origin. In this work we investigate the role of initial coherence on entanglement dynamics of a spatially separated two qubit system in a common vacuum reservoir with dipolar interaction. We construct two classes of X states, namely, states with one photon coherence ( X 1 ) and states with two photon coherence ( X 2 ). Considering them as initial states, we study entanglement dynamics under Markov approximation. We find for states in X 1 , ESD time, revival time and time over which the state remains disentangled increase with increase in coherence. On the other hand for states in X 2 , with increase in coherence ESD time increases, revival time remains same and time of disentanglement decreases. Thus, states with two photon coherence are better resources for applications since their entanglement is robust against decoherence compared to states with one photon coherence.

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Quantum Control of Finite-time Disentanglement in Qubit-Qubit and Qubit-Qutrit Systems

Mazhar Ali

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.

•Jan 1, 2009•1 citation
Entanglement is a fundamental concept in quantum mechanics. In this review, we study various aspects of coherence and entanglement, illustrated by several examples. We relate the concepts of loss of coherence and disentanglement, via a model of two two-level atoms in different types of reservoir, including cases of both independent and common baths. Finally, we relate decoherence and disentanglement, by focusing on the sudden death of the entanglement and the dependence of the death time with the distance of our initial condition from the decoherence-free subspace. In particular, we study the sudden death of the entanglement in a two-atom system with a common reservoir.
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.
"or many years the entangled systems have been associated to the quantum world, while the separable systems with the classical world. Recently quantum discord showed that some separable states posses quantum correlation even when the entanglement is zero. In this work, we compare different features of quantum discord and entanglement of formation for two qubits in a common squeezed reservoir. We relate the quantum correlations with the “distance” of our initial condition from the decoherence free subspace where the system is not affected by environment. While for some initial conditions, the entanglement presents sudden death and revival, quantum discord does not. Still, is not clear the relation between these two measurements of “quantumness”."
We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.
Abstract Bipartite entanglement is a necessary resource in most processes in quantum information science. Decoherence resulting from the interaction of the bipartite system with environment not only degrades the entanglement, but can result in abrupt disentanglement, known as entanglement sudden death (ESD). In some cases, a subsequent revival of entanglement is also possible. ESD is an undesirable feature for the state to be used as a resource in applications. In order to delay or avoid ESD, it is necessary to understand its origin. In this work we investigate the role of initial coherence on entanglement dynamics of a spatially separated two qubit system in a common vacuum reservoir with dipolar interaction. We construct two classes of X states, namely, states with one photon coherence ( X 1 ) and states with two photon coherence ( X 2 ). Considering them as initial states, we study entanglement dynamics under Markov approximation. We find for states in X 1 , ESD time, revival time and time over which the state remains disentangled increase with increase in coherence. On the other hand for states in X 2 , with increase in coherence ESD time increases, revival time remains same and time of disentanglement decreases. Thus, states with two photon coherence are better resources for applications since their entanglement is robust against decoherence compared to states with one photon coherence.
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.