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Journal of Russian Laser Research

Reduction of the density matrix and tomography analysis of the two-particle spin-state structure

V. A. Andreev

Published Sep 1, 2007• 0 citations
Publisher
DOI
10.1007/s10946-007-0037-0

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A new “classical” formulation of conventional quantum mechanics is used to construct a description of quantum states with spin j =1/2 which uses only positive classical probabilities of observables instead of a complex density matrix. These probabilities are functions of points on a unit sphere which determine the directions relative to which the spin projections are measured. The proposed construction is a generalization of a system for tomography of the spin states of a single particle and may be used as a new method of measuring two-particle spin states. For pure spin states this method is exactly the same as the case of a single particle. Additional probabilities must be defined to describe mixed states.
The right hand side of Bell inequalities don’t depend on a form of any two‐particle spin state. In the case of the generalized Bell‐Clauser‐Horne‐Schimony‐Holt inequalities the right hand side depend on a form of concrete two‐particle state. The left hand sides of these inequalities depend on four arbitrary vectors defined in three‐dimensional space. They define directions on which spins of particles forming a correlated pair are projected. Our aim is to find such vectors that left‐hand side of the inequality should takes its maximum value. In other words on these vectors the inequality transforms into equality. It is shown that it can be done with the help of special reduction of density matrix of two‐state spin state.
Procedures of the preparation and detection of entangled electron-nuclear spin states in (15)N@C(60) by combining electron spin resonance and electron nuclear double resonance pulse techniques are presented. A quantitative evaluation of the complete density matrix is obtained by a special density matrix tomography. All four Bell states of a two qubit subsystem were analyzed and experimental decoherence times are presented. In addition, we estimate a quantum critical temperature of T(q)=7.76 K for this system at an electron spin resonance frequency of 95 GHz.