Quantum correlations and tomographic representation

Tomographic discord for a system of two coupled nanoelectric circuits

“…The validity of the two-qubit approximation estimated by parameter (36) is presented on Fig. 3(c)-(d), respectively.…”

“…Clearly, the tomographic approach generalizes the Shannon information theory on the quantum domain in a very natural way. In the past few decades, a wide class of problems in quantum information theory, e.g., revealing new inequalities for Shannon [28] and Rényi entropies [29][30][31], tomographic approach to the Bell-type inequalities [32], quantumness tests [33], quantum correlations and quantum discord [31,[34][35][36], has been investigated in detail [37].…”

Subadditivity Condition for Spin Tomograms and Density Matrices of Arbitrary Composite and Noncomposite Qudit Systems

“…In view of this, the inequalities known for classical probability distributions can be obtained also for quantum tomograms [12][13][14][15][16][17]. A recent review of the probability-vector properties both in classical and quantum domains is presented in [18].…”

Probability Representation of Quantum Observables and Quantum States

“…The tomographic probabilities identified with quantum states can be associated with density operators, in view of the formalism of star-product quantization [35,36,37,38,39] analogous to the procedure where the phase-space quasidistributions of quantum states, like the Wigner function, are presented within the star-product framework in [40] (see also recent reviews [41,42]). On the other hand, quantum observables associated with Hermitian operators are presented within the star-product framework by symbols of the operators, which are some functions on the phase space, say, in the Wigner-Weyl representation or the functions of discrete variables in the spin-tomographic description of qudit states.…”

“…We derive the evolution equation for quantum observables (Heisenberg equation) in the probability representation and give examples of the spin-1/2 (qubit) states and the spin observables. We present quantum channels for qubits in the probability representation.developed to obtain the formulation of quantum states more similar to the formulation of the states in classical statistical mechanics.Recently, the tomographic probability representation of quantum states was suggested [12]; in this representation, the quantum states are identified with fair probability distributions connected with density matrices in its phase-space representations by integral transforms; e.g., the Radon transform [13] of the Wigner function provides the optical tomogram [14,15], which is a standard probability distribution of continuous homodyne quadrature of photon depending on an extra parameter called the local oscillator phase, which can be measured [16].The probability distributions determining the spin states were considered in [17,18,19,20,21,22,23,24], and the tomographic probability representation of quantum states was studied in [25,26,27,28,29,30,31,32,33,34].The tomographic probabilities identified with quantum states can be associated with density operators, in view of the formalism of star-product quantization [35,36,37,38,39] analogous to the procedure where the phase-space quasidistributions of quantum states, like the Wigner function, are presented within the star-product framework in [40] (see also recent reviews [41,42]). On the other hand, quantum observables associated with Hermitian operators are presented within the star-product framework by symbols of the operators, which are some functions on the phase space, say, in the Wigner-Weyl representation or the functions of discrete variables in the spin-tomographic description of qudit states.The ...…”