In order to put the characteristic polynomial of a density matrix in a new form we use a result of A. J. Mountain. The coefficients of the characteristic polynomial in this form are functions of a new class of invariants introduced by K. Lendi. These invariants are expressed using the symmetric and scalar product for the Bloch vector associated with the density matrix. The conversion relations from the Bloch vectors to the Fano parameters allow us the calculation of Lendi’s invariants as functions of the Fano parameters. We obtain also the beautiful result of Horodeckis [16] about the factorization of the characteristic equation of a two-qubits density matrix.In order to put the characteristic polynomial of a density matrix in a new form we use a result of A. J. Mountain. The coefficients of the characteristic polynomial in this form are functions of a new class of invariants introduced by K. Lendi. These invariants are expressed using the symmetric and scalar product for the Bloch vector associated with the density matrix. The conversion relations from the Bloch vectors to the Fano parameters allow us the calculation of Lendi’s invariants as functions of the Fano parameters. We obtain also the beautiful result of Horodeckis [16] about the factorization of the characteristic equation of a two-qubits density matrix.

Jan 1, 20050 citations

Calculating generating functions from characteristic functions, with application to quantum optics

Edward B. Rockower, N. B. Abraham

A method is found for calculating the number generating function of a harmonic oscillator density matrix directly from the quantum characteristic function. This technique is used to interpret thermal noise in a model for an optical detector. The results clearly reveal an earlier misinterpretation and emphasise that the terminal noise is a statistically independent amplitude in the detector/harmonic oscillator which is superposed with an amplitude having the same statistical nature as the incident optical field.A method is found for calculating the number generating function of a harmonic oscillator density matrix directly from the quantum characteristic function. This technique is used to interpret thermal noise in a model for an optical detector. The results clearly reveal an earlier misinterpretation and emphasise that the terminal noise is a statistically independent amplitude in the detector/harmonic oscillator which is superposed with an amplitude having the same statistical nature as the incident optical field.

Journal of Physics A Mathematical and GeneralOct 1, 197810 citations

Density Matrix Theory and Applications

Bernd Esser

Zeitschrift für Physikalische ChemieJan 1, 19980 citations

Density Matrix Theory and Applications

Karl Blum

Springer eBooksJan 1, 19811,121 citations

Photon-counting distribution in squeezed states

Apostol Vourdas, Richard M. Weiner

We calculate the counting (multiplicity) distribution ${P}_{N}=〈N|\ensuremath{\rho}|N〉$ where $\ensuremath{\rho}$ is (i) the density matrix corresponding to a (pure) squeezed state and (ii) the density matrix of a superposition of squeezed states with thermal light. In the first case, we find that ${P}_{N}$ is an oscillating function of $N$ . In the second case, this behavior, characteristic for squeezed states, disappears even for small amounts of noise.We calculate the counting (multiplicity) distribution ${P}_{N}=〈N|\ensuremath{\rho}|N〉$ where $\ensuremath{\rho}$ is (i) the density matrix corresponding to a (pure) squeezed state and (ii) the density matrix of a superposition of squeezed states with thermal light. In the first case, we find that ${P}_{N}$ is an oscillating function of $N$. In the second case, this behavior, characteristic for squeezed states, disappears even for small amounts of noise.

Physical Review ADec 1, 198796 citations

{P}_{N}

is an oscillating function of

N

. In the second case, this behavior, characteristic for squeezed states, disappears even for small amounts of noise.