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Journal of Physics B Atomic Molecular and Optical Physics

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

C. V. Namitha, S. V. M. Satyanarayana

Published Jan 9, 2018• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/aaa65a

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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.
In this paper, the origin of disentanglement for two specific sub-classes of [Formula: see text]-states namely maximally nonlocal mixed states (MNMSs) and maximally entangled mixed states (MEMSs) is investigated analytically for a physical system consisting of two spatially separated qubits interacting with a common vacuum bath. The phenomena of entanglement sudden death (ESD) and the entanglement sudden birth (ESB) are observed, but the characteristics of ESD and ESB are found to be different for the case of two-photon coherence and single photon coherence states. The role played by initial coherence for the underlying entanglement dynamics is investigated. Further, the entanglement dynamics of MNMSs and MEMSs under different environmental noises namely phase damping, amplitude damping and random telegraph noise (RTN) noise with respect to the decay and revival of entanglement is analyzed. It is observed that the single photon coherence states are more robust against the sudden death of entanglement, indicating the usability of such states in the development of technologies for the practical implementation of quantum information processing tasks.
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.
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
The decoherence of two initially entangled qubits coupled with a squeezed vacuum cavity separately is investigated exactly. The results show that, first, in principle, the disentanglement time decreases with the increase of squeeze parameter r, due to the augmenting of average photon number of every mode in the squeezed vacuum cavity. Second, there appear entanglement revivals after the complete disentanglement for the case of even parity initial Bell state, while there occur the entanglement decrease and the entanglement revival before the complete disentanglement for the case of odd parity initial Bell state. The results are quite different from those for the case of qubits in a vacuum cavity.
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 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.