相关论文: Simple Minimal Informationally Complete Measuremen…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…
Measurement is integral to quantum information processing and communication; it is how information encoded in the state of a system is transformed into classical signals for further use. In quantum optics, measurements are typically…
Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and…
Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we…
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical…
A number of atomic beam experiments, related to the Ramsey experiment and a recent experiment by Brune et al., are studied with respect to the question of complementarity. Three different procedures for obtaining information on the state of…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
The concept of intrinsic and operational observables in quantum mechanics is introduced. It is argued that, in any realistic description of a quantum measurement that includes a detecting device, it is possible to construct from the…
Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators…
We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of…
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
Let $\lambda\in \mathbb{R},$ $\mu\in \mathbb{R}$ and $B$ be a linear bounded operator from a Hilbert space $\mathcal{K}$ into another Hilbert space $\mathcal{H}.$ In this paper, we consider the formulas of the absolute value…
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality…
We justify that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to the dimension of the density matrix in the Fock representation. Using this as our thread, we…
We introduce a non real-valued measure on the definable sets contained in the finite part of a cartesian power of an o-minimal field $R$. The measure takes values in an ordered semiring, the Dedekind completion of a quotient of $R$. We show…
We obtain a complete characterization of the weak-type $(1,1)$ for Haar shift operators in terms of generalized Haar systems adapted to a Borel measure $\mu$ in the operator-valued setting. The main technical tool in our method is a…
Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…
We propose an all-optical implementation of quantum-information processing in semiconductor quantum dots, where electron-hole excitations (excitons) serve as the computational degrees of freedom (qubits). The strong dot confinement leads to…
Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…