We examine the stochastic dynamics of entanglement for an uncoupled two-qubit system, undergoing continuous parity measurement. Starting with a fully mixed state, the entanglement is zero for a finite amount of time, when it is suddenly created, which we refer to as entanglement genesis. There can be further entanglement sudden death or birth events culminating in the formation of a fully entangled state. We present numerical investigations of this effect together with statistics of the entanglement genesis time in the weak measurement limit as well as the quantum Zeno limit. An analytic treatment of the physics is presented, aided by the derivation of a simple concurrence equation for Bell basis
X states. The probability of entanglement border crossing and mean first passage times are calculated for the case of measurement dynamics alone. We find that states with almost the same probability of entanglement border crossing can have very different average crossing times. Our results provide insight on the optimization of entanglement generation by measurement.
Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced between the qubits, and build an energetic-based estimator to assess the presence of entanglement in the circuit. Remarkably, this estimator is valid at the single-trajectory level and shows to be robust against finite detection efficiency. Our work paves the road towards a fundamental understanding of the stochastic energetic processes associated with entanglement genesis, and opens new perspectives for witnessing quantum correlations thanks to quantum thermodynamic quantities.
Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced between the qubits, and build an energetic-based estimator to assess the presence of entanglement in the circuit. Remarkably, this estimator is valid at the single-trajectory level and shows to be robust against finite detection efficiency. Our work paves the road towards a fundamental understanding of the stochastic energetic processes associated with entanglement genesis, and opens new perspectives for witnessing quantum correlations thanks to quantum thermodynamic quantities.