Related papers: Restricted numerical range: a versatile tool in th…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm…
We investigate the spectral properties of the volume operator in quantum gravity in the framework of a previously introduced lattice discretization. The presence of a well-defined scalar product in this approach permits us to make definite…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations…
We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
To simulate a quantum system with continuous degrees of freedom on a quantum computer based on quantum digits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to discrete observables. We consider this…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
We analyze the properties of the conditional amplitude operator, the quantum analog of the conditional probability which has been introduced in [quant-ph/9512022]. The spectrum of the conditional operator characterizing a quantum bipartite…
This paper investigates new properties of $q$-numerical ranges for compact normal operators and establishes refined upper bounds for the $q$-numerical radius of Hilbert space operators. We first prove that for a compact normal operator $T$…
Quantum capacity quantifies the amount of quantum information that can be transmitted by a quantum channel with an arbitrary small probability of error. Mathematically, the quantum capacity is given by an asymptotic formula involving the…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved…
In the complex action theory whose path runs over not only past but also future we study a normalized matrix element of an operator $\hat{\cal O}$ defined in terms of the future state at the latest time $T_B$ and the past state at the…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by a non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity can be restored via an amended inner-product metric $\Theta$. In…
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an…