Inverse spin-s portrait and representation of qudit states by single probability vectors

Abstract

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j + 1)(4j + 1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere S 2 . Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j + 3) simplex, with the boundary being illustrated for qubits (j = 1/2) and qutrits (j = 1). A relation to the (2j + 1) 2 -and (2j + 1)(2j + 2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.

Minkowski-Type Inequality for Arbitrary Density Matrices of Composite and Noncomposite Systems

“…the tomographic probability representation of quantum states [12][13][14][15][16][17]. In this representation, which is valid for both discrete and continuous variables [12], the spin states (qudit states) are identified with fair tomographic probability distributions [18][19][20][21]. In view of this fact, the standard formulas for classical probability distributions like the formulas for entropy and information can be easily compared with the corresponding quantum relationships [22,23].…”

Wigner Functions and Spin Tomograms for Qubit States

“…In this paper, we present the one-qubit case. We study in detail a concrete example of the qubit state, using explicit forms of the quantizer and dequantizer determining the tomographic probability distribution given in [32]. This paper is organized as follows.…”

Finite Phase Space, Wigner Functions, and Tomography for Two-Qubit States

“…We study in detail a concrete example of two-qubit states using explicit forms of quantizer and dequantizer determining the tomographic-probability distribution found in [20]. This paper is organized as follows.…”