We provide a study of various quantum phase transitions occurring in the XY Heisenberg chain in a transverse magnetic field using the Meyer-Wallach measure of (global) entanglement. We obtain analytic expression of the measure for finite-size systems, and show that it can be used to obtain critical exponents via finite-size scaling with great accuracy for the Ising universality class. We also calculate an analytic expression for the isotropic (XX) model and show that global entanglement can precisely identify the level-crossing points. The critical exponent for the isotropic transition is obtained exactly from an analytic expression for global entanglement in the thermodynamic limit. Next, the general behavior of the measure is calculated in the thermodynamic limit considering the important role of symmetries for this limit. The so-called oscillatory transition in the ferromagnetic regime can only be characterized by the thermodynamic limit where global entanglement is shown to be zero on the transition curve. Finally, the anisotropic transition is explored where it is shown that global entanglement exhibits an interesting behavior in the finite size limit. In the thermodynamic limit, we show that global entanglement shows a cusp-singularity across the Ising and anisotropic transition, while showing non-analytic behavior at the XX multi-critical point. It is concluded that global entanglement can be used to identify all the rich structure of the ground state Heisenberg chain.
We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact (PC), which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, the mixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.
In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on onedimensional regular networks. For this purpose, we assume that every node is represented by a quantum dot continuously monitored by an individual point contact (Gurvitz's model). This measuring process induces decoherence. We focus on small rates of decoherence and then obtain the mixing time bound of the CTQWs on the one-dimensional regular network, whose distance parameter is l ! 2. Our results show that the mixing time is inversely proportional to the rate of decoherence, which is in agreement with the mentioned results for cycles in Refs. 29 and 37. Also, the same result is provided in Ref. 38 for long-range interacting cycles. Moreover, we¯nd that this quantity is independent of the distance parameter l ðl ! 2Þ and that the small values of decoherence make short the mixing time on these networks. 795 Int. J. Quantum Inform. 2010.08:795-806. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/15/15. For personal use only. Ne ÀÀ NÀ1 N t : ð37Þ E®ect of Decoherence on Mixing Time in CTQWs 803 Int. J. Quantum Inform. 2010.08:795-806. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/15/15. For personal use only.
Finding the energy levels of a quantum system is a significant task, for instance, to characterize the compatibility of materials or to analyze reaction rates in drug discovery and catalysis. In this paper we investigate quantum metrology, the research field focusing on the estimation of unknown parameters investigating quantum resources, to address this problem for a three-level system interacting with laser fields. The performance of simultaneous estimation of the levels compared to independent one is also studied in various scenarios. Moreover, we introduce the Hilbert-Schmidt speed (HSS), a mathematical tool, as a powerful figure of merit for enhancing the estimation of the energy spectrum. This measure can be easily computed, since it does not require diagonalizing the density matrix of the system, verifying its efficiency to enhance quantum estimation in high-dimensional systems.
In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its 2l nearest neighbors(l on either side). In our investigation, the nodes of network are represented by a set of identical tunnel-coupled quantum dots in which decoherence is induced by continuous monitoring of each quantum dot with nearby point contact detector. To formulate the decoherent CTQWs, we use Gurvitz model and then calculate probability distribution and the bounds of instantaneous and average mixing times. We show that the mixing times are linearly proportional to the decoherence rate. Moreover, adding links to cycle network, in appearance of large decoherence, decreases the mixing times.
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