Related papers: Quantum State Reconstruction From Incomplete Data
Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…
We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a…
Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the…
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…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete…
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
We revisit quantum tomography in an informationally incomplete scenario and propose improved state reconstruction methods using deep neural networks. In the first approach, the trained network predicts an optimal linear or quadratic…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state…
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…
A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that…