Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing

In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented

Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system, is itself asymptotically Gaussian and compute its quantum Fisher information which sets an absolute bound to the estimation error. The classical and quantum Fisher informations are compared in a simple example. In the vicinity of $\theta=0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localised in the system, while the output is independent of the parameter.Comment: 10 pages, 2 figures. final versio

Global information balance in quantum measurements

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with post-selection, is briefly discussed.Comment: Final version to appear on Physical Review Letter

Statistical analysis on testing of an entangled state based on Poisson distribution framework

A hypothesis testing scheme for entanglement has been formulated based on the Poisson distribution framework instead of the POVM framework. Three designs were proposed to test the entangled states in this framework. The designs were evaluated in terms of the asymptotic variance. It has been shown that the optimal time allocation between the coincidence and anti-coincidence measurement bases improves the conventional testing method. The test can be further improved by optimizing the time allocation between the anti-coincidence bases.Comment: This paper is an extended version of the theoretical part of v1 of quant-ph/0603254.quant-ph/0603254 is revised so that it is more familiar to experimentalist

Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

We discuss two quantum analogues of Fisher information, symmetric logarithmic derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher information from a large deviation viewpoint of quantum estimation and prove that the former gives the true bound and the latter gives the bound of consistent superefficient estimators. In another comparison, it is shown that the difference between them is characterized by the change of the order of limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st

One-loop unitarity of scalar field theories on Poincare invariant commutative nonassociative spacetimes

We study scalar field theories on Poincare invariant commutative nonassociative spacetimes. We compute the one-loop self-energy diagrams in the ordinary path integral quantization scheme with Feynman's prescription, and find that the Cutkosky rule is satisfied. This property is in contrast with that of noncommutative field theory, since it is known that noncommutative field theory with space/time noncommutativity violates unitarity in the above standard scheme, and the quantization procedure will necessarily become complicated to obtain a sensible Poincare invariant noncommutative field theory. We point out a peculiar feature of the non-locality in our nonassociative field theories, which may explain the property of the unitarity distinct from noncommutative field theories. Thus commutative nonassociative field theories seem to contain physically interesting field theories on deformed spacetimes.Comment: 25 pages, 9 figures ; appendix and references adde

Path Integral for Space-time Noncommutative Field Theory

The path integral for space-time noncommutative theory is formulated by means of Schwinger's action principle which is based on the equations of motion and a suitable ansatz of asymptotic conditions. The resulting path integral has essentially the same physical basis as the Yang-Feldman formulation. It is first shown that higher derivative theories are neatly dealt with by the path integral formulation, and the underlying canonical structure is recovered by the Bjorken-Johnson-Low (BJL) prescription from correlation functions defined by the path integral. A simple theory which is non-local in time is then analyzed for an illustration of the complications related to quantization, unitarity and positive energy conditions. From the view point of BJL prescription, the naive quantization in the interaction picture is justified for space-time noncommutative theory but not for the simple theory non-local in time. We finally show that the perturbative unitarity and the positive energy condition, in the sense that only the positive energy flows in the positive time direction for any fixed time-slice in space-time, are not simultaneously satisfied for space-time noncommutative theory by the known methods of quantization.Comment: 21 page

Hypothesis testing for an entangled state produced by spontaneous parametric down conversion

Generation and characterization of entanglement are crucial tasks in quantum information processing. A hypothesis testing scheme for entanglement has been formulated. Three designs were proposed to test the entangled photon states created by the spontaneous parametric down conversion. The time allocations between the measurement vectors were designed to consider the anisotropic deviation of the generated photon states from the maximally entangled states. The designs were evaluated in terms of the p-value based on the observed data. It has been experimentally demonstrated that the optimal time allocation between the coincidence and anti-coincidence measurement vectors improves the entanglement test. A further improvement is also experimentally demonstrated by optimizing the time allocation between the anti-coincidence vectors. Analysis on the data obtained in the experiment verified the advantage of the entanglement test designed by the optimal time allocation.Comment: 7 figures, 9 pages. This paper is revised for increasing the readership for experimentalists. Hence, the mathematical part is moved to a new manuscript quant-ph/060802

Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebra.Comment: 13p LaTeX Document (should be run twice

Dispersion Relations for Thermally Excited Waves in Plasma Crystals

Thermally excited waves in a Plasma crystal were numerically simulated using a Box_Tree code. The code is a Barnes_Hut tree code proven effective in modeling systems composed of large numbers of particles. Interaction between individual particles was assumed to conform to a Yukawa potential. Particle charge, mass, density, Debye length and output data intervals are all adjustable parameters in the code. Employing a Fourier transform on the output data, dispersion relations for both longitudinal and transverse wave modes were determined. These were compared with the dispersion relations obtained from experiment as well as a theory based on a harmonic approximation to the potential. They were found to agree over a range of 0.9<k<5, where k is the shielding parameter, defined by the ratio between interparticle distance a and dust Debye length lD. This is an improvement over experimental data as current experiments can only verify the theory up to k = 1.5.Comment: 8 pages, Presented at COSPAR '0