Related papers: Half a state, half an operator: a general formulat…
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…
Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest, which are unfeasible for classical computers. Recent developments in quantum technology enable the precise control of individual…
On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…
A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for…
We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators,…
We study homological structure of the filtrations of the spaces of self-adjoint operators by the multiplicity of the ground state. We consider only operators acting in a finite dimensional complex or real Hilbert space but infinite…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of a Hilbert space into two subspaces 1 and 2 is an amount of information, which can be transmitted through 1 and 2…
A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the $N$ agents has the access to regenerate the original state with two local unitary operations if…
Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to…
Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different…
We formulate one dimensional many-body integrable systems in terms of a new set of phase space variables involving exchange operators. The hamiltonian in these variables assumes a decoupled form. This greatly simplifies the derivation of…
A system s behavior is typically specified through models such as state diagrams that describe how the system should behave. According to researchers, it is not clear what a state actually represents regarding the system to be modeled.…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…