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تسجيل مستخدم جديدMajorization relation in quantum critical systems
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The most basic local conversion is local operations and classical communications (LOCC), which is also the most natural restriction in quantum information processing. We investigate the
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Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wavefunctions. Realistic quantum systems are coupled however often to m
ore than one continuum. For example, the conductance of an open cavity needs at least two environments, namely the input and the output channel. In the present paper, we study generic features of the transfer of particles through an open quantum system coupled to two channels. We compare the results with those characteristic of a one-channel system. Of special interest is the parameter range which is influenced by singular points. Here, the states of the system are mixed via the environment. In the one-channel case, the resonance structure of the cross section is independent of the existence of singular points. In the two-channel case, however, new effects appear caused by coherence. An example is the enhanced conductance of an open cavity in a certain finite parameter range. It is anti-correlated with the phase rigidity of the eigenfunctions of the non-Hermitian Hamilton operator.
The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the uncertaint
y relations which mainly focus on the pure states. Here we present an experimental investigation on the optimal majorization uncertainty for mixed states by means of the coherent light. The polarization states with adjustable mixedness are prepared by the combination of two coherent beams, and we test the majorization uncertainty relation for three incompatible observables using the prepared mixed states. The experimental results show that the direct sum majorization uncertainty relations are tight and optimal for general mixed systems.
The Lipkin-Meshkov-Glick (LMG) model describes critical systems with interaction beyond the first-neighbor approximation. Here we address the characterization of LMG systems, i.e. the estimation of anisotropy, and show how criticality may be exploite
d to improve precision. In particular, we provide exact results for the Quantum Fisher Information of small-size LMG chains made of $N=2, 3$ and $4$ lattice sites and analyze the same quantity in the thermodynamical limit by means of a zero-th order approximation of the system Hamiltonian. We then show that the ultimate bounds to precision may be achieved by tuning the external field and by measuring the total magnetization of the system. We also address the use of LMG systems as quantum thermometers and show that: i) precision is governed by the gap between the lowest energy levels of the systems, ii) field-dependent level crossing provides a resource to extend the operating range of the quantum thermometer.
We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our approach pr
ovides a significant improvement of the uncertainty bound compared with previous majorization-based approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111, 230401 (2013); A. E. Rastegin and K. .Zyczkowski, J. Phys. A, 49, 355301 (2016)], particularly by extending the direct-sum majorization relation first introduced in [L. Rudnicki, Z. Pucha{l}a and K. .{Z}yczkowski, Phys. Rev. A 89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations by considering a pair of qubit observables in a two-dimensional system and randomly chosen unsharp observables in a three-dimensional system. We also demonstrate that our bound tends to be stronger than the generalized Maassen--Uffink bound with an increase in the unsharpness effect. Furthermore, we extend our approach to the case of multiple POVM measurements, thus making it possible to establish entropic uncertainty relations involving more than two observables.
Uncertainty relation is not only of fundamental importance to quantum mechanics, but also crucial to the quantum information technology. Recently, majorization formulation of uncertainty relations (MURs) have been widely studied, ranging from two mea
surements to multiple measurements. Here, for the first time, we experimentally investigate MURs for two measurements and multiple measurements in the high-dimensional systems, and study the intrinsic distinction between direct-product MURs and direct-sum MURs. The experimental results reveal that by taking different nonnegative Schur-concave functions as uncertainty measure, the two types of MURs have their own particular advantages, and also verify that there exists certain case where three-measurement majorization uncertainty relation is much stronger than the one obtained by summing pairwise two-measurement uncertainty relations. Our work not only fills the gap of experimental studies of majorization uncertainty relations, but also represents an advance in quantitatively understanding and experimental verification of majorization uncertainty relations which are universal and capture the essence of uncertainty in quantum theory.
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