Quantum trajectories and their statistics for remotely entangled quantum bits

TL;DR

This paper combines experimental and theoretical methods to analyze quantum trajectories of remotely monitored entangled transmon qubits, revealing entanglement dynamics, trajectory classes, and maximal concurrence boundaries.

Contribution

It provides the first detailed experimental and theoretical analysis of quantum trajectories for remote entanglement generation in superconducting qubits, including path probabilities and entanglement limits.

Findings

Quantum trajectories split into low and high entanglement classes.

Distribution of concurrence exhibits a sharp cut-off at maximal entanglement.

Most likely paths project the system into specific subspaces.

Abstract

We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noise limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes corresponding to half-parity collapse. The distribution of concurrence is found at any given time and we explore the dynamics of entanglement creation in the state space. The distribution exhibits a sharp cut-off in the high concurrence limit, defining a maximal concurrence boundary. The most likely paths of the qubits' trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace. We also investigate the most likely time for the individual trajectories to reach their most entangled state, and find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes. The theoretical predictions show excellent agreement with the experimental entangled qubit trajectory data.