Generation of concurrence between two qubits locally coupled to a one-dimensional spin chain

Abstract

We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance d. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of d when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for d = 0, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by d as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate. We further show that the maximally and minimally decohering channels show singular behavior which can be explained by invoking upon a quasi-particle picture.

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

“…Focusing on our work, the model considered here is referred as the generalized central spin model (GCSM) where two qubits are locally coupled to the environmental spin chain. It noteworthy that the sudden quench is also employed in the environmental clean spin chain to study the generation of concurrence [13] and decay of concurrence [39] between a pair of qubits considering GCSM.…”

“…In recent year, there has been an upsurge of studies in various quantum information theoretic measures such as fidelity [1], decoherence [2,3], concurrence [4,5], quantum discord [6] and entanglement entropy [7] connecting the quantum information science [8][9][10][11][12][13][14], statistical physics and condensed matter physics [15][16][17][18] in a concrete way. In particular, the eect of quantum criticality appears in the ground-state correlation that becomes maximum at the quantum critical point (QCP); for example, the concurrence, a separability based approach to measure the quantum correlation, can detect as well as characterize a QCP.…”

Entanglement entropy of a three-spin-interacting spin chain with a time-reversal-breaking impurity at one boundary

“…Study of various quantum information theoretic measures such as fidelity [1], decoherence [2,3], concurrence [4,5], quantum discord [6] and entanglement entropy (EE) [7] has grabbed immense attention as it connects the quantum information science [8][9][10][11][12][13][14], statistical physics and condensed matter physics [15][16][17][18] in a concrete way. All of the above quantities are able to capture the ground state singularity and thus are used as indicators of quantum phase transition (QPT).…”

Phase transitions and thermal entanglement of the distorted Ising–Heisenberg spin chain: topology of multiple-spin exchange interactions in spin ladders

“…Quantum spin chains as the most well-studied quantum models of statistical mechanics exhibit a wide variety of attractive phenomena at zero temperature such as the quantum phase transitions, which are driven by the change of the external parameters at absolute zero temperature [1][2][3], and also at low temperatures [4] that are controlled by the behavior of their ground states and low lying excited states. Entanglement [5,6] is one of the most interesting of such quantum phenomena, as it is a fundamental resource in performing most tasks in quantum computation and quantum information processing [7][8][9][10]. The relations between the ground state phase transitions and the quantum entanglement have already been revealed for the classes of spin-1/2 Heisenberg models [2,[11][12][13].…”

“…Entanglement [5,6] is one of the most interesting of such quantum phenomena, as it is a fundamental resource in performing most tasks in quantum computation and quantum information processing [7][8][9][10]. The relations between the ground state phase transitions and the quantum entanglement have already been revealed for the classes of spin-1/2 Heisenberg models [2,[11][12][13].…”