相关论文: Simple Minimal Informationally Complete Measuremen…
We study the spectral properties of positive absolutely minimum attaining operators defined on infinite dimensional complex Hilbert spaces and using that derive a characterization theorem for such type of operators. We construct several…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…
It has been recently shown that an observable that identifies all pure states of a d-dimensional quantum system has minimally 4d-4 outcomes or slightly less (the exact number depending on the dimension d). However, no simple construction of…
Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. Central to this capacity is their role as tomographically complete measurements with the…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
The study of how to generate high-dimensional quantum states (qudits) is justified by the advantages that they can bring for the field of quantum information. However, to have some real practical potential for quantum communication, these…
The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the…
We derive an exact expression for the quantumness of a Hilbert space (defined in quant-ph/0302092), and show that in composite Hilbert spaces the signal states must contain at least some entangled states in order to achieve such a…
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is…
Let $\mathbb{P}$ be the complete metric space consisting of positive invertible operators on an infinite-dimensional Hilbert space with the Thompson metric. We introduce the notion of operator means of probability measures on $\mathbb{P}$,…
We show that a general linear transformation from one single photon qudit to another, the dimension of which can be either equal or unequal to that of the first one, can be implemented by linear optics. As an application of the scheme we…
Quantum measurements are our eyes to the quantum systems consisting of a multitude of microscopic degrees of freedom. However, the intrinsic uncertainty of quantum measurements and the exponentially large Hilbert space pose natural barriers…
We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). For informationally complete sets, we propose construction methods from orthonormal Hermitian operator…
A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…
For a quantum measurement process described by a quantum instrument $\mathcal{I}$ and a system observable corresponding to a positive-operator valued measure (POVM) $E ,$ $\mathcal{I}$ is said to conserve the information of $E$ if the joint…
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. It is far less common to exploit non-Hermitian operators to perform measurements. Here, we show…
Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible…
In quantum theory, a physical observable is represented by a Hermitian operator as it admits real eigenvalues. This stems from the fact that any measuring apparatus that is supposed to measure a physical observable will always yield a real…
Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are…