Berlin 2015 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 2: Quanteninformation

MP 2.1: Talk

Tuesday, March 17, 2015, 10:55–11:15, HFT-FT 101

From discrete to continuous: finite dimensional approximations of continuous variables — •Michael Keyl — TU München, Fakultät Mathematik

Small fluctuations of a finite ensemble of qubits behave in the infinite particle limit like a continuous quantum system. This behavior is usually studied in terms of expectation values: Expectation values of certain fluctuation operators Q_N, P_N of a finite system converge for N → ∞ against corresponding expectation values of canonical position and momentum Q and P. In this talk we will show that the finite dimensional quantities are related to the continuous variables in a much stronger sense, namely that the spectral measures of Q_N and P_N converge weakly against the spectral measures of Q, P. To derive this result we use the recently studied Schwartz operators, i.e. trace class operators which stay in the trace class after products with arbitrary polynomials in P and Q. They are a perfect framework for the discussion of operator moment problems, and provide in addition powerful methods to study quadratic forms in terms of distributions.