Quantum Trajectories and Their Statistics for Remotely Entangled Quantum Bits

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. 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 cutoff 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, conforming to a "half-parity" measurement. We also investigate the most-likely time for the individual trajectories to reach their most entangled state, and we 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.

Quantum Bayesian approach to circuit QED measurement with moderate bandwidth

“…Such a generalization is useful to describe the process of entanglement of superconducting qubits by measurement [51,52,77,78]. For N qubits the state of the system can be described in the way similar to Eq.…”

Simultaneous continuous measurement of noncommuting observables: Quantum state correlations

“…(23)- (24). To find such correlators, we introduce the two-sided joint probability density W 2 for the quantum state to reach the states q 1 at time t 1 and q 2 at time t 2 ≥ t 1 given that the initial state is q in at time t 0 and the final state is q f at time T ,…”

Symmetries and physically realisable ensembles for open quantum systems

“…is not, however, the only way-we will provide an example in the following subsection for which 0 R is not invariant. |, it is clear that a 7 The effect of having a constraint on the number of Lindblad channels-in particular of having L<D−1-will be explored in future work [40].…”

“…Questions of this type [1] may offer novel insights into the nature of open quantum system dynamics and the quantum-classical epistemic distinction [2][3][4]. The observation of single quantum trajectories has now been realised in the laboratory [5][6][7][8][9], with ever increasing detection efficiencies [10]. Additionally, there is strong theoretical evidence for the stability of the particular class of quantum trajectories under consideration [11].…”