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We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and…
We identify optimal measurement strategies for phase estimation in different scenarios. For pure states of a single qubit, we show that optimal measurements form a broad set parametrized with a continuous variable. When the state is mixed…
Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this…
Quantum state tomography seeks to reconstruct an unknown state from measurement statistics. A finite measurement (POVM) is \emph{pure-state informationally complete} (PSI-Complete) if the outcome probabilities determine any pure state up to…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
We address the "major open problem" of evaluating how much increased efficiency in estimation is possible using non-separable, as opposed to separable, measurements of N copies of m-level quantum systems. First, we study the six cases m =…
We present an efficient method to solve the quantum discord of two-qubit X states exactly. A geometric picture is used to clarify whether and when the general POVM measurement is superior to von Neumann measurement. We show that either the…
We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
We consider the problem of deciding whether a given state preparation, i.e., a source of quantum states, is accurate, namely produces states close to a target one within a prescribed threshold. We show that, when multiple measurements need…
Efficient verification of quantum states and gates is crucial to the development of quantum technologies. Although the sample complexities of quantum state verification and quantum gate verification have been studied by many researchers,…
We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all…
We develop a practical quantum tomography protocol and implement measurements of pure states of ququarts realized with polarization states of photon pairs (biphotons). The method is based on an optimal choice of the measuring scheme's…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…