On quantum information
On quantum information
We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator ��, tr ��=1. Let I(P)\in R be defined for any partition P = (P_1,...,P_m), P_1+ ... +P_m=1_H, P_i \in proj H$ and let I(P_i Qj, i \leq m, j \leq n) = I(P) + I(Q) for Q =(Q_1,..., Q_n), \sum Q_j = 1_H and P_iQ_j = Q_j P_i, tr �� P_iQ_j = tr �� P_i tr �� Q_j (P, Q are physically independent). Assuming some continuity properties we give a general form of generalised information I.
20 pages
FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, Primary 81P45, Secondary 60A10, 47B65, 94A17, 46C07
FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), FOS: Physical sciences, Mathematical Physics (math-ph), Mathematical Physics, Primary 81P45, Secondary 60A10, 47B65, 94A17, 46C07
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