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arXiv:2401.16921

Effect of repeated projective measurements on a two-qubit system undergoing dephasing

Hammas Hussain Ali, Muhammad Abdullah Ijaz, Fariha Hassan, Diya Batool, Adam Zaman Chaudhry

Published Jan 30, 2024• 0 citations
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Abstract

The entanglement dynamics of an exactly solvable, pure dephasing model are studied. Repeated projective measurements are performed on the two-qubit system. Due to the system-environment interaction, system-environment correlations are established between each measurement. Consequently, the environment state keeps evolving. We investigate the effect of this changing environment state on the entanglement dynamics. In particular, we compare the dynamics with the case where the environment state is repeatedly reset.

DOI
10.48550/arxiv.2401.16921

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The entanglement dynamics of an exactly solvable, pure dephasing model are studied. Repeated projective measurements are performed on the two-qubit system. Due to the system-environment interaction, system-environment correlations are established between each measurement. Consequently, the environment state keeps evolving. We investigate the effect of this changing environment state on the entanglement dynamics. In particular, we compare the dynamics with the case where the environment state is repeatedly reset.
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We consider a qubit coupled to another system (its environment) and discuss the relationship between the effects of subjecting the qubit to either a dynamical decoupling sequence of unitary operations or a sequence of projective measurements. We give a formal statement concerning the equivalence of a sequence of coherent operations on a qubit, precisely operations from a minimal set ${{\mathbb{1}}_{Q},{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}}$, and a sequence of projective measurements of observable ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$. Using it we show that when the qubit is subjected to nnn such successive projective measurements at certain times, the expectation value of the last measurement can be expressed as a linear combination of expectation values of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ observed after subjecting the qubit to dynamical decoupling sequences of $\ensuremath{\pi}$ pulses, with $k\ensuremath{\le}n$ of them applied at subsets of these times. Performing a sequence of measurements on the qubit gives then access to the same properties of the environment and qubit-environment coupling that are affecting the coherence observed in a dynamical decoupling experiment. Analyzing the latter has been widely used to characterize the environmental dynamics (perform so-called noise spectroscopy), so our result shows how the results obtained with dynamical-decoupling-based protocols are related to those that can be obtained just by performing multiple measurements on the qubit. We also discuss in more detail the application of the general result to the case of the qubit undergoing pure dephasing and outline possible extensions to higher-dimensional systems (a qudit or multiple qubits).
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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.
We study the coherence and quantum correlations for a system consisting of two interacting qubits under the effect of a common environment, where the system of qubits has the dephasing coupling with its surrounding. We study the dynamical behaviour of the quantumness measures when the influence of the qubits’ interaction on the dephasing is analyzed. We display the effect of the qubit-qubit interaction and qubits-environment interaction on the measures considering the case of symmetry and asymmetry interaction between the qubits and environment. Finally, we explicitly illustrate the relation between the coherence and quantum correlations and show that quantum coherence and correlations can be preserved during the dynamics.
We study the exact entanglement dynamics of two qubits coupled to a common bosonic reservoir through a pure dephasing interaction. We ask how this dynamics changes when the qubits and the reservoir already share correlations before the qubit state is prepared. In that case the system and reservoir first interact for a long time and settle into a joint equilibrium state. Only afterward is the qubit pair projected onto the desired state by a local measurement. For an Ohmic spectral density we obtain the exact reduced two qubit dynamics. Using the Wootters concurrence we show that initial correlations always speed up entanglement sudden death relative to the factorized case, and that this gap grows quadratically with the coupling strength in the weak-to-moderate coupling regime. Finally we show that a symmetric sequence of periodic π pulses applied to both qubits extends the entanglement lifetime close to a factor of seven over the range of pulse numbers studied.