Related papers: Quantum tomography via Non-orthogonal basis and we…
Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as…
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…
Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…
We propose an experiment which demonstrates the undoing of a weak continuous measurement of a solid-state qubit, so that any unknown initial state is fully restored. The undoing procedure has only a finite probability of success because of…
Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Quantum sensing exploits quantum phenomena to enhance the detection and estimation of classical parameters of physical systems and biological entities, particularly so as to overcome the inefficiencies of its classical counterparts. A…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
We present an error analysis of various tomographic protocols based on the linear inversion for the reconstruction of an unknown two-qubit state. We solve the problem of finding a tomographic protocol which is the most robust against errors…
The use of weak measurements for performing quantum tomography is enjoying increased attention due to several recent proposals. The advertised merits of using weak measurements in this context are varied, but are generally represented by…
Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In…
The concept of a \emph{weak value} of a quantum observable was developed in the late 1980s by Aharonov and colleagues to characterize the value of an observable for a quantum system in the time interval between two projective measurements.…
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state new information is continually mapped onto the measured…
The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…
We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and…