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Register a new userViscous control of minimum uncertainty state
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T. Koide
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A minimum uncertainty state for position and momentum is obtained in quantum viscous hydrodynamics which is defined through the Navier-Stokes-Korteweg (NSK) equation. This state is the generalization of the coherent state and its uncertainty is given by a function of the coefficient of viscosity. The uncertainty can be smaller than the standard minimum value in quantum mechanics, $hbar/2$, when the coefficient of viscosity is smaller than a critical value which is similar in magnitude to the Kovtun-Son-Starinets (KSS) bound.
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Squeezing experiments which are capable of creating a minimum uncertainty state during the nonlinear process, for example optical parametric amplification, are commonly used to produce light far below the quantum noise limit. This report presents a method with which one can characterize this minimum uncertainty state and gain valuable knowledge of the experimental setup.
We address the question, does a system A being entangled with another system B, put any constraints on the Heisenberg uncertainty relation (or the Schrodinger-Robertson inequality)? We find that the equality of the uncertainty relation cannot be reached for any two noncommuting observables, for finite dimensional Hilbert spaces if the Schmidt rank of the entangled state is maximal. One consequence is that the lower bound of the uncertainty relation can never be attained for any two observables for qubits, if the state is entangled. For infinite-dimensional Hilbert space too, we show that there is a class of physically interesting entangled states for which no two noncommuting observables can attain the minimum uncertainty equality.
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In NMR (Nuclear Magnetic Resonance) quantum computation, the selective control of multiple homonuclear spins is usually slow because their resonance frequencies are very close to each other. To quickly implement controls against decoherence effects, this paper presents an efficient numerical algorithm fordesigning minimum-time local transformations in two homonuclear spins. We obtain an accurate minimum-time estimation via geometric analysis on the two-timescale decomposition of the dynamics. Such estimation narrows down the range of search for the minimum-time control with a gradient-type optimization algorithm. Numerical simulations show that this method can remarkably reduce the search efforts, especially when the frequency difference is very small and the control field is high. Its effectiveness is further demonstrated by NMR experiments with two homunuclear carbon spins in a trichloroethylene (C2H1Cl3) sample system.
New uncertainty relations for n observables are established. The relations take the invariant form of inequalities between the characteristic coefficients of order r, r = 1,2,...,n, of the uncertainty matrix and the matrix of mean commutators of the observables. It is shown that the second and the third order characteristic inequalities for the three generators of SU(1,1) and SU(2) are minimized in the corresponding group-related coherent states with maximal symmetry.
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