Related papers: Phase retrievability of frames and quantum channel…
We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states.…
In this paper we introduce EPOSIC channels, a class of SU(2)-covariant quantum channels. We give their definition, a Kraus representation of them, and compute their Choi matrices. We show that these channels form the set of extreme points…
Pilot-aided channel estimation is nowadays a standard component in each wireless receiver enabling coherent transmission of complex-valued constellations, only affected by noise and interference. Whenever these disturbances are sufficiently…
In this work we propose a simple optical architecture, based on phase-only programmable spatial light modulators, in order to characterize general processes on photonic spatial quantum systems in a $d>2$ Hilbert space. We demonstrate the…
In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame…
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…
Extracting classical information from quantum systems is an essential step of many quantum algorithms. However, this information could be corrupted as the systems are prone to quantum noises, and its distortion under quantum dynamics has…
Reachability analysis plays a central role in system design and verification. The reachability problem, denoted $\Diamond^J\,\Phi$, asks whether the system will meet the property $\Phi$ after some time in a given time interval $J$.…
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
A pair of quantum channels are said to be incompatible if they cannot be realized as marginals of a single channel. This paper addresses the general structure of the incompatibility of completely positive channels with a fixed quantum input…
We consider the problem of high-dimensional channel estimation in fast time-varying millimeter-wave MIMO systems with a hybrid architecture. By exploiting the low-rank and sparsity properties of the channel matrix, we propose a two-phase…
Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
In this paper we present a necessary and sufficient condition of distinguishability of bipartite quantum states. It is shown that the operators to reliably distinguish states need only rounds of projective measurements and classical…
In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this…