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Recent results have established dramatic advantages in learning properties of quantum states when a quantum computer is available to process or jointly measure multiple copies of the unknown quantum state. Learning tasks can be accomplished…
In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < \eta \leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed…
Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A 71, 050301(R) (2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior…
Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number…
For the precise estimation of the unknown quantum state, the independent samples should be prepared. Can we reduce the error of the estimation by the measurement using the quantum correlation between every sample? In this paper, this…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and…
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…
Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data,…
We propose a refined iterative likelihood-maximization algorithm for reconstructing a quantum state from a set of tomographic measurements. The algorithm is characterized by a very high convergence rate and features a simple adaptive…
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the on-line choice of optimal measurements allows to reach the ultimate bounds of…
To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…
Here, we study the problem of decoding information transmitted through unknown quantum states. We assume that Alice encodes an alphabet into a set of orthogonal quantum states, which are then transmitted to Bob. However, the quantum channel…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
As often emerges in various basic quantum properties such as R\'enyi and Tsallis entropies, the trace of quantum state powers $\text{tr}(\rho^q)$ has attracted a lot of attention. The recent work of Liu and Wang (SODA 2025) showed that,…
State estimation is usually analyzed in the situation when copies are in a product state, either mixed or pure. We investigate here the concept of state estimation on correlated copies. We analyze state estimation on correlated N qubit…
We give a rigorous treatment on the foundation of the first order asymptotic theory of quantum estimation, with tractable and reasonable regularity conditions. Different from past works, we do not use Fisher information nor MLE, and an…
Approximating the $k$-th spectral gap $\Delta_k=|\lambda_k-\lambda_{k+1}|$ and the corresponding midpoint $\mu_k=\frac{\lambda_k+\lambda_{k+1}}{2}$ of an $N\times N$ Hermitian matrix with eigenvalues…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…