Continuous joint measurement and entanglement of qubits in remote cavities

TL;DR

This paper provides a comprehensive theoretical analysis of entangling two remote superconducting qubits via continuous measurement in microwave cavities, highlighting conditions for persistent entanglement and robustness against imperfections.

Contribution

It introduces a first-principles approach using the SLH formalism to model continuous measurement and entanglement of remote qubits, including effective stochastic master equations and pulse shaping strategies.

Findings

Entanglement can be maintained continuously with shaped pulses.

The entanglement robustness persists despite measurement imperfections.

Tradeoffs between simulation representations affect non-Markovian dynamics.

Abstract

We present a first-principles theoretical analysis of the entanglement of two superconducting qubits in spatially separated microwave cavities by a sequential (cascaded) probe of the two cavities with a coherent mode, that provides a full characterization of both the continuous measurement induced dynamics and the entanglement generation. We use the SLH formalism to derive the full quantum master equation for the coupled qubits and cavities system, within the rotating wave and dispersive approximations, and conditioned equations for the cavity fields. We then develop effective stochastic master equations for the dynamics of the qubit system in both a polaronic reference frame and a reduced representation within the laboratory frame. We compare simulations with and analyze tradeoffs between these two representations, including the onset of a non-Markovian regime for simulations in the reduced representation. We provide conditions for ensuring persistence of entanglement and show that using shaped pulses enables these conditions to be met at all times under general experimental conditions. The resulting entanglement is shown to be robust with respect to measurement imperfections and loss channels. We also study the effects of qubit driving and relaxation dynamics during a weak measurement, as a prelude to modeling measurement-based feedback control in this cascaded system.