Qubit-environment entanglement in time-dependent pure dephasing for transmon qubits


We generalized the methods for quantification of system-environment entanglement that were previously developed for interactions that lead to pure decoherence (PD) of the system for time-independent Hamiltonians to time-dependent Hamiltonians. We have shown that the if-and-only-if criteria of separability [1], the entanglement measure [2], and the methods of detecting entanglement through operations and measurements performed only on the system without access to the environment [3] generalize in a straightforward manner to the case of time-dependent Hamiltonians. Thus the theoretical study of this type of entanglement is straightforward, while the time-dependence can enable experimental detection of entanglement for a wider class of PD interactions. The methods were used to study the evolution of system-environment entanglement of a transmon qubit interacting with microwave cavity photons [4] for an interaction switching between an entangling and a non-entangling one. This allows us to study nontrivial dependencies between the buildup of classical and quantum correlations, as the buildup of entanglement does not directly follow the switching of the interaction [5]. Furthermore, we show how to detect entanglement in this system, which is undetectable by the time-independent methods due to symmetries in the Hamiltonian, by taking advantage of the controllable time-dependence of the interaction.

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[2] K. Roszak, Measure of qubit-environment entanglement for pure dephasing evolutions, Phys. Rev. Research 2, 043062 (2020).
[3] M. Strzałka and K. Roszak, Detection of entanglement during pure dephasing evolutions for systems and environments of any size, Phys. Rev. A 104, 042411 (2021).
[4] P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys-Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf, et al., Quantum error correction of a qubit encoded in grid states of an oscillator, Nature 584, 368 (2020).
[5] M. Strzałka, R. Filip, and K. Roszak, Qubit-environment entanglement in time-dependent pure dephasing, Phys. Rev. A 109, 032412 (2024).