169 research outputs found
Physical symmetries and gauge choices in the Landau problem
Due to a special nature of the Landau problem, in which the magnetic field is
uniformly spreading over the whole two-dimensional plane, there necessarily
exist three conserved quantities, i.e. two conserved momenta and one conserved
orbital angular momentum for the electron, independently of the choice of the
gauge potential. Accordingly, the quantum eigen-functions of the Landau problem
can be obtained by diagonalizing the Landau Hamiltonian together with one of
the above three conserved operators with the result that the quantum mechanical
eigen-functions of the Landau problem can be written down for arbitrary gauge
potential. The purpose of the present paper is to clarify the meaning of gauge
choice in the Landau problem based on this gauge-potential-independent
formulation, with a particular intention of unraveling the physical
significance of the concept of gauge-invariant-extension of the canonical
orbital angular momentum advocated in recent literature on the nucleon spin
decomposition problem. At the end, our analysis is shown to disclose a
physically vacuous side face of the gauge symmetry.Comment: version to appear in The European Physical Journal
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
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
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