ﻻ يوجد ملخص باللغة العربية
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new general formalism describing the unitary evolution of a qudit $(dgeq2)$ in terms of the Bloch-like vector space and specify how in a general case this formalism is related to finding time-dependent parameters in the exponential representation of the evolution operator under an arbitrary time-dependent Hamiltonian. Applying this new general formalism to a qubit case $(d=2)$, we specify the unitary evolution of a qubit via the evolution of a unit vector in $mathbb{R}^{4}$ and this allows us to derive the precise analytical expression of the qubit unitary evolution operator for a wide class of nonstationary Hamiltonians. This new analytical expression includes the qubit solutions known in the literature only as particular cases.
We formulate and prove the main properties of the generalized Gell-Mann representation for traceless qudit observables with eigenvalues in $[-1,1]$ and analyze via this representation violation of the CHSH inequality by a general two-qudit state. For
The Gell-Mann grading, one of the four gradings of sl(3,C) that cannot be further refined, is considered as the initial grading for the graded contraction procedure. Using the symmetries of the Gell-Mann grading, the system of contraction equations i
This article summarizes some of the most important scientific contributions of Murray Gell-Mann (1929-2019). (Invited article for Current Science, Indian Academy of Sciences.)
A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl-Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separabl
In this paper, by utilizing the idea of stabilizer codes, we give some relationships between one local unitary representation of braid group in N-qubit tensor space and the corresponding entanglement properties of the N-qubit pure state $|Psirangle$,