Entanglement genesis under continuous parity measurement

Abstract

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/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 insights on the optimization of entanglement generation by measurement.PACS numbers: 03.65. Ta,03.65.Yz Entanglement is arguably the most fascinating aspect of quantum mechanics and plays a central role in quantum information science. The peculiar non-classical correlations which entanglement characterizes are the basis for exciting applications such as teleportation, quantum encryption, and many others [1]. Since the concept of entanglement appeared, there has been much research into its properties. One aspect of this research has been how to quantify the amount of entanglement contained in a quantum state. Many different entanglement measures have been introduced with varying degrees of success [2]. In the two qubit case, the concurrence measure of entanglement can be explicitly given in general for any mixed state [3], making this system ideal for further research.In parallel with these measures, investigations into the dynamics of entanglement began and continue still. If entanglement is to be used as a resource, then its dynamical evolution must be understood. Of particular interest is how entanglement decays when the entangled systems are coupled to the environment. It was found that entanglement typically decreases at an exponential rate, faster than single-qubit decoherence [4,5,6,7]. An important step was the realization by Jakóbczyk [8] and Yu and Eberly [9] that entanglement can reach zero in a finite time. This behavior was dubbed "entanglement sudden death" [9,10,11,12,13,14,15] and has received much recent attention. The ability of entanglement to have this non-analytic behavior can be traced back to its definition: two particles are considered entangled if their combined density matrix cannot be decomposed into a weighted sum of pure, separable density matrices. If such a decomposition can be found, then it is defined to be seperable, having zero entanglement. While it is important to understand the disappearance of entanglement, we must also understand how it is generated in the first place. This is the topic d...

Quantum Trajectories and Their Statistics for Remotely Entangled Quantum Bits

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“…Measurement-induced entanglement of spatially separated quantum systems is a startling prediction of quantum mechanics [1][2][3][4][5][6][7]. Recent experiments have demonstrated this effect via single-photon heralding [8][9][10][11], as well as via continuous measurement of photons interacting with qubits [12].…”

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Entanglement Genesis by Ancilla-Based Parity Measurement in 2D Circuit QED

“…[34]. The finite time to entanglement observed in serial timing is reminiscent of the entanglement genesis time required under continuous parity measurement.…”