Physics – Quantum Physics
Scientific paper
2003-10-03
J.Russ.Laser Res. 24 (2003) 507-543
Physics
Quantum Physics
Latex, material of talk at conference in Bregenz, July 2003, accepted for publication by Journal of Russian Laser Research
Scientific paper
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying the adjoint representation. Positive maps of density operator are related to random matrices. The tomographic probability description of quantum states is used to formulate the problem of separability and entanglement as the condition for joint probability distribution of several random variables represented as the convex sum of products of probabilities of random variables describing the subsystems. The property is discussed as a possible criterion for separability or entanglement. The convenient criterion of positivity of finite and infinite matrix is obtained. The U(n)-tomogram of a multiparticle spin state is introduced. The entanglement measure is considered in terms of this tomogram.
Man'ko Vladimir I.
Marmo Giuseppe
Sudarshan E. C. G.
Zaccaria Francesco
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