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arXiv:1605.07430 · Quantum Information and Computation

The entangling power of a glocal dissipative map

Alireza Nourmandipour, Mohammad Kazem Tavassoly, Stefano Mancini

Published Sep 1, 2016• 8 citations
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Abstract

We consider a model of two qubits dissipating into both local and global environments (generally at non-zero temperatures), with the possibility of interpolating between purely local dissipation and purely global one. The corresponding dissipative dynamical map is characterized in terms of its Kraus operators focusing on the stationary regime. We then determine conditions under which entanglement can be induced by the action of such a map. It results (rather counterintuitively) that in order to have entanglement in the presence of local environment, this latter must be at nonzero temperature.

DOI
10.26421/qic16.11-12-3

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We consider a model of two qubits dissipating into both local and global environments (generally at non-zero temperatures), with the possibility of interpolating between purely local dissipation and purely global one. The corresponding dissipative dynamical map is characterized in terms of its Kraus operators focusing on the stationary regime. We then determine conditions under which entanglement can be induced by the action of such a map. It results (rather counterintuitively) that in order to have entanglement in the presence of local environment, this latter must be at nonzero temperature.
In this paper, we investigate the possibility of entanglement swapping between two distinct qubits coupled to their own (in general) non-Markovian environments. This goal is achieved by performing Bell state measurement on photons leaving dissipative cavities. In the continuation, we introduce the concept of entangling power to measure the average of swapped entanglement over all possible pure initial states. Then we present our results in two regimes, strong and weak coupling, and discuss the role of the detuning parameter in each regime in the amount of swapped entanglement. We also determine the conditions under which the maximum amount of entanglement can be swapped between the two qubits. It is revealed that, despite the presence of dissipation, it is possible to create long-living stationary entanglement between the two qubits.
In this paper, we review some results concerning the dissipative dynamics of two coupled qubits interacting with independent reservoirs. In particular, we focus on the role of counter-rotating terms in the qubit-qubit coupling, showing that their presence is the origin of stationary entanglement, which also turns out to be robust with respect to temperature. We also discuss the performances of different non-Markovian approaches in the description of the qubit-qubit dynamics, by considering a simplified exactly solvable Hamiltonian model.
We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian, while the other two qubits are isolated, i.e., do not interact with environment, directly. Then, the time evolution of the density matrix (for the pure as well as mixed initial density matrix) and the corresponding reduced density matrices are obtained, by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.
Consider a bipartite quantum system S=AB such that each part interacts only with its local environment. Under such circumstances, one expects that the entanglement between parts A and B does not increase after the time evolution. In fact, this is the case if the reduced dynamics of the system is given by EA⊗EB\mathcal{E}_{A}\otimes \mathcal{E}_{B}EA​⊗EB​, where EA\mathcal{E}_{A}EA​ and EB\mathcal{E}_{B}EB​ are quantum channels, i.e., completely positive trace-preserving maps. But, the reduced dynamics of the system may be given by a map as ΨA⊗ΨBΨ_{A}\otimes Ψ_{B}ΨA​⊗ΨB​, where ΨAΨ_{A}ΨA​ and ΨBΨ_{B}ΨB​ are local non-positive maps. Then, the entanglement between A and B can exceed its initial value, as was shown in the case studied by Jordan et al. [Phys. Rev. A 76, 022102 (2007)]. In this paper, we first explore the general circumstances under which one can find such cases as they found. Next, we introduce another general procedure which leads to local non-positive maps that exhibit entanglement exceeding. Furthermore, we demonstrate that this apparent entanglement increase in the two above procedures corresponds physically to the retrieval of pre-existing inaccessible entanglement stored across the global system-environment degrees of freedom, rather than genuine generation of the entanglement ex nihilo\textit{ex nihilo}ex nihilo.
Two non-directly interacting qubits with equal frequencies can become entangled via a Markovian, dissipative dynamics through the action of a weakly coupled Ohmic heat bath. In the standard weak-coupling limit derivation, this purely dissipative effect disappears if the frequencies are different because of the “ergodic average” used by this approach. However, there are physical situations where this technique is too rough to capture all the relevant aspects of the dissipative dynamics. In these cases, in order to better describe the physical behavior of the open system, it is necessary to go beyond the “ergodic average”. We show that, in this more refined framework, the entanglement capability of the environment persists also in the case of different frequencies.
We investigate to what extent a suitably chosen system Hamiltonian can counteract local dissipative processes and preserve entanglement in the stationary state. The results determine prospects and limitations of dissipative state preparation schemes based on natural dissipative processes---in contrast to engineered, typically nonlocal dissipative schemes. As an exemplary case, we determine the stationary state of two spontaneously decaying two-level systems with optimal entanglement properties. The corresponding system Hamiltonian is derived, and its possible experimental implementation is discussed in detail. Finally, we discuss generalizations for NNN qubits.