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We consider the vector space of $n times n$ matrices over $mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying matrices. The commutators, anticommutators, and the eigenvalue problem of such operators are also discussed. Other matrix functions such as the exponential functions are studied. Density operators and Kraus operators are also discussed.
In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semidefinite operator ?, is defined in terms of the d2 coherent states in this system. The Choquet integral CQ of the Q-function, is introduced using a ranki
We have proposed and demonstrated a general and scalable scheme for programmable unitary gates. Our method is based on matrix decomposition into diagonal and Fourier factors. Thus, we are able to construct arbitrary matrix operators only by diagonal
In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by the name of assemblage moment matrices (AMMs) has been introduced for the device-independent quantification of quantum steerability and measurement incompatibility. In other
Starting with an adjoint pair of operators, under suitable abstra
Noise sequences of infinite matrices associated with covariant phase and box localization observables are defined and determined. The canonical observables are characterized within the relevant classes of observables as those with asymptotically mini