Related papers: On Estimating the State of a Finite Level Quantum …
A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…
Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is constant equal to the inverse $1/\sqrt{d}$, with $d$ the dimension of the finite Hilbert space, are becoming more and…
An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems.…
In the problem of quantum state tomography, one is given $n$ copies of an unknown rank-$r$ mixed state $\rho \in \mathbb{C}^{d \times d}$ and asked to produce an estimator of $\rho$. In this work, we present the debiased Keyl's algorithm,…
An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of…
We investigate the estimation technique called quantum state smoothing introduced by Guevara and Wiseman [Phys.~Rev.~Lett.~{\bf 115}, 180407 (2015)], which offers a valid quantum state estimate for a partially monitored system, conditioned…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
We investigate the extent to which we can establish whether or not two quantum systems have been prepared in the same state. We investigate the possibility of universal unambiguous state comparison. We show that it is impossible to…
We propose a general approach to characterize states of a bipartite system composed by a fully controllable and an unaccessible subsystems. The method is based on the measuring interference between states of the uncontrollable subsystem…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von…
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state…
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, "Ancilla", system as proposed by Allahverdyan, Balian and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)].…
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet…
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance (NMR) setup and employing geometric discord, we evaluate the quantum correlations of a…