Related papers: On Single Qubit Quantum State Tomography
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE)…
Quantum measurement plays a crucial role in quantum metrology. Due to the limitations of experimental capabilities, collectively measuring multiple copies of probing systems can present significant challenges. Therefore, the concept of…
Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method…
We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal…
The minimum probability of error (MPE) measurement discriminates between a set of candidate quantum states with the minimum average error probability allowed by quantum mechanics. Conditions for a measurement to be MPE were derived by Yuen,…
The maximum-likelihood method for quantum estimation is reviewed and applied to the reconstruction of density matrix of spin and radiation as well as to the determination of several parameters of interest in quantum optics.
Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, QST becomes impractical for reconstructing multi-qubit density matrices since data sets and computational costs grow exponentially with qubit…
We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an $O ( ( 1 / k ) \log D )$ rate, where $k$ denotes the number of…
The minimum Kullback entropy principle (mKE) is a useful tool to estimate quantum states and operations from incomplete data and prior information. In general, the solution of a mKE problem is analytically challenging and an approximate…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system by using the error matrix method. It is found that the state tomography method determines well the parameters that are…
Amplitude Estimation (AE) is a critical subroutine in many quantum algorithms, allowing for a quadratic speedup in various applications like those involving estimating statistics of various functions as in financial Monte Carlo simulations.…
Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choice in estimating quantum…
A major bottleneck in the quest for scalable many-body quantum technologies is the difficulty in benchmarking their preparations, which suffer from an exponential `curse of dimensionality' inherent to their quantum states. We present an…
Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. To accommodate the diverse characteristics of quantum chemical systems,…
The determination of the density matrix of an ensemble of identically prepared quantum systems by performing a series of measurements, known as quantum tomography, is minimal when the number of outcomes is minimal. The most accurate minimal…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…
Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In…