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Journal of Physics A Mathematical and Theoretical

Interference of qubits in pure dephasing and almost pure dephasing environments

Marcin Łobejko, Marcin Mierzejewski, Jerzy Dajka

Published Jun 16, 2015• 4 citations
Publisher

Abstract

Two-path interference of quantum particles with internal spin (qubits) interacting on one arm of the interferometer with bosonic environment is studied. It is assumed that the energy exchange between the qubit and its environment is either absent, which is a pure dephasing (decoherence) model, or very weak. Both the amplitude and the position of maximum of an output intensity discussed as a function of a phase shift can serve as a quantifier of parameters describing coupling between qubit and its environment. The time evolution of the qubit–environment system is analyzed in the Schrödinger picture and the output intensity for qubit–environment interaction close to pure decoherence is analyzed by means of perturbation theory. Quality of the applied approximation is verified by comparison with numerical results.

DOI
10.1088/1751-8113/48/27/275302

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Two-path interference of quantum particles with internal spin (qubits) interacting on one arm of the interferometer with bosonic environment is studied. It is assumed that the energy exchange between the qubit and its environment is either absent, which is a pure dephasing (decoherence) model, or very weak. Both the amplitude and the position of maximum of an output intensity discussed as a function of a phase shift can serve as a quantifier of parameters describing coupling between qubit and its environment. The time evolution of the qubit–environment system is analyzed in the Schrödinger picture and the output intensity for qubit–environment interaction close to pure decoherence is analyzed by means of perturbation theory. Quality of the applied approximation is verified by comparison with numerical results.
Ultrafast spectroscopy is a valuable tool for monitoring the timescales of interactions between systems and their environments, resulting in pure dephasing. The superposition of ground and excited states of a molecule in a condensed phase, created by field–matter interactions, loses its coherence due to fluctuations from surrounding molecules that interact differently with the ground and excited states. Recently, quantum decoherence has become an intense area of research due to its relevance to the quantum-to-classical transition and its critical role in developing quantum technologies, such as quantum computers and cryptography. Although both pure dephasing and quantum decoherence result from the same process of environmental monitoring of systems through quantum entanglement between the system and its environment, they have been studied and discussed in very different contexts with seemingly disparate terminologies. In this work, we present a detailed theoretical description of pure dephasing and quantum decoherence in bosonic environments coupled to a two-level system, compare them directly, and demonstrate their connections to the wave–particle duality of isolated systems and the wave-particle-entanglement triality of composite systems consisting of systems and their environments. It is believed that the present review will be helpful for gaining a deeper understanding of ultrafast spectroscopy from a quantum mechanical perspective and the wave–particle duality of quantum objects interacting with their surrounding environments.
Decoherence of qubits is one main limitation in quantum information processing, where the qubits themselves can be mixed because of decoherence and additional decoherence may generated through interactions with a bath. Here, we present a complete study of qubit-environment entanglement in the case of interactions that lead to pure dephasing of the qubit by allowing the initial state of the qubit to be mixed, exceeding previous restrictions. We find that the criteria for separability that hold for pure initial states of the qubit are reduced to witness status. Yet, the evolution of the witnesses reflects the array of features that entanglement can exhibit in the mixed case but are forbidden in the pure-qubit case. Most notably, this includes sudden birth of entanglement as the initial phase of the evolution is typically separable. Moreover, there is a stark numerical advantage to the study of entanglement for large environments when using the witness rather than the traditional measures available. We include the study of entanglement generated between a spin qubit and a sparse spin environment to illustrate the peculiarities of the evolution of entanglement in this case, as well as to emphasize the level of reliability of the entanglement witness.
In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian bath within the pure dephasing spin-boson model. First, using this model, we analytically establish the previously anticipated similarity between the non-equilibrium and the equilibrium correlation functions Px(t)P_x(t)Px​(t) and Cx(t)C_x(t)Cx​(t). Then, in the short/long time asymptotic behaviors of Px(t)P_x(t)Px​(t), we find singular dependence on AAA (coupling strength) and sss (bath exponent) at their integer values. Finally, we find that the non-Hermitian bath tends to suppress the decoherence of qubit for all values of AAA and sss, in contrast to the conclusion of Dey et al. . Our results show the potential of non-Hermitian environment engineering in suppressing the decoherence of qubit.
Abstract In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian environment within the pure dephasing spin-boson model. Using this model, we analytically establish the previously anticipated similarity between the non-equilibrium and the equilibrium correlation functions Px(t)P_x(t)Px​(t) and Cx(t)C_x(t)Cx​(t). We find that integer values of AAA (coupling strength) or sss (bath exponent) has distinctive long time asymptotic behaviors of Px(t)P_x(t)Px​(t) and Cx(t)C_x(t)Cx​(t) from those of the non-integer values, accompanied with a diverging crossover time scale. We also find that the non-Hermitian environment tends to suppress the decoherence of qubit for all values of AAA and sss, in contrast to the conclusion of Dey et al . [Phys. Lett. A 383, 125931 (2019)]. Our results show the potential of the non-Hermitian environmental engineering for suppressing the decoherence of qubit.
One of the main frameworks to analyze the effects of the environment in a quantum computer is that of pure dephasing, where the dynamics of qubits can be characterised in terms of a well-known dynamical map. In this work we present a non-peturbative extension of such map beyond this simple pure-dephasing case, i.e. that is valid for a general spin coupled to a bosonic environment in a thermal state. To this aim, we use a Trotter decomposition and a Magnus expansion to simplify the unitary evolution operator in interaction picture. The proposed derivation can be extended to other finite-level open quantum systems including many body, initial system-environment correlated states, multiple-time correlation functions or quantum information protocols.
Abstract We propose a scheme for the detection of qubit–environment entanglement which requires only operations and measurements on the qubit, all within reach of current experimental state-of-the-art. The scheme works for any type of interaction which leads to pure dephasing of the qubit as long as the initial qubit state is pure. The scheme is direct in the sense that it allows the detection of entanglement present in the system at time τ\tau τ τ after the initialization of the qubit in a superposition state. It requires a measurement on the qubit at time τ\tau τ τ and a comparison of the post-measurement evolution to the evolution obtained by a modified scheme. It becomes particularly simple when one of the qubit states is neutral with respect to the environment, such as in case of the most common choice of the NV center spin qubit or for excitonic charge qubits, when the environment is initially at thermal equilibrium. In this case, the post-measurement evolution needs to be compared only to the standard decoherence which is obtained without any qubit manipulation after the preparation of the initial state.