Related papers: Convex approximations of quantum channels
We consider the problem of optimally approximating an unavailable quantum state $\rho $ by the convex mixing of states drawn from a set of available states $\{ \nu_i\}$. The problem is recast to look for the least distinguishable state from…
We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…
A unified framework is proposed in this paper for parameter estimation using convex optimization and experiment design applying convex maximization for Pauli channels, that can be extended to generalized Pauli channels, too. In the case of…
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…
In a recent paper, M. F. Sacchi [Phys. Rev. A 96, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show…
We investigate the problem of optimally approximating a desired state by the convex mixing of a set of available states. The problem is recasted as finding the optimal state with the minimum distance from target state in a convex set of…
We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for…
Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex…
Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels,…
We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that…
Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
The optimal measurement configuration, i.e., the optimal input quantum state and measurement in the form of a POVM with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined…
We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in…
Approximating a quantum state by the convex mixing of some given states has strong experimental significance and provides potential applications in quantum resource theory. Here we find a closed form of the minimal distance in the sense of…
Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional…
We address the question of finding the most effective convex decompositions into boundary elements (so-called boundariness) for sets of quantum states, observables and channels. First we show that in general convex sets the boundariness…
A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…