Continuous measurements of two qubits

TL;DR

This paper develops a theory for continuous quantum measurements of two interacting qubits, analyzing how detector non-linearity and qubit interactions affect spectral features and measurement limitations.

Contribution

It introduces a comprehensive theoretical framework for understanding continuous measurement of two qubits, including effects of detector non-linearity and qubit interactions on spectral signals.

Findings

Spectral peaks at combination frequencies due to non-linearity.

Interaction shifts and splits spectral peaks for identical qubits.

Quantum measurement limits peak heights in the spectrum.

Abstract

We develop a theory of coherent quantum oscillations in two, in general interacting, qubits measured continuously by a mesoscopic detector with arbitrary non-linearity and discuss an example of SQUID magnetometer that can operate as such a detector. Calculated spectra of the detector output show that the detector non-linearity should lead to mixing of the oscillations of the two qubits. For non-interacting qubits oscillating with frequencies $\Omega_1$ and $\Omega_2$, the mixing manifests itself as spectral peaks at the combination frequencies $\Omega_1\pm \Omega_2$. Additional nonlinearity introduced by the qubit-qubit interaction shifts all the frequencies. In particular, for identical qubits, the interaction splits coherent superposition of the single-qubit peaks at $\Omega_1=\Omega_2$. Quantum mechanics of the measurement imposes limitations on the height of the spectral peaks.