Quantum Zeno stabilization in weak continuous measurement of two qubits

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...

Section: Analytical Approachmentioning

confidence: 77%

Section: Even Paritymentioning

confidence: 99%

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Entanglement genesis under continuous parity measurement

Williams

Jordan

2008

“…Checking ever more frequently whether the system is indeed inside one eventually destroys the transitions between and the rest of the Hilbert space. Thus, because of the Zeno effect, a continuously observed system [5] prepared inside would spend there all available time, while for a system initially outside , τ would be exactly zero [6]. Alternatively, one can perform a finite time measurement of τ in which a meter monitors the system over a finite period of time, and one single observation is made at the end of the run.…”

Section: Introductionmentioning

confidence: 99%

Zeno effect and ergodicity in finite-time quantum measurements

Sokolovski

2011

We demonstrate that an attempt to measure a non-local in time quantity, such as the time average $\la A\ra_T$ of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator $\a$. Conversely, in a long measurement of $\la A\ra_T$ to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which von Neumann ensemble average of $\a$ coincides with $\la A\ra_T$. Both effects are conveniently analysed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behaviour is shown to be a consequence of conservation of probability

“…Several authors have investigated projective measurements either as a way to achieve universality [23] or as a means of entangling electrons in mesoscopic devices [15,24,25,26,27,28]. An extensive study of projective measurements of electrons in double quantum dots has been made in [27,28], in which various aspects of the geometry involved and the effect of asymmetry were discussed.…”

Section: A General Setupmentioning

confidence: 99%

Entangling spins by measuring charge: A parity-gate toolbox

Ionicioiu

2007

The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyse the parity gate (P -gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with P -gates and show that native networks simplify considerably the resources required for producing multi-qubit entanglement, like n-GHZ states. Other applications include a Bell-state analyser and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin n-GHZ state with linear elements (beam-splitters and local spin-flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct a novel spin CZ-gate by using the mode degrees of freedom as ancillae.