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Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables…
The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic…
We report the close form expressions of the photon number statistics for a generalized coherent state and a generalized photon-added coherent state, which are shown to be crucial for proposing a variety of quantum scissor operations. The…
State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
Phase insensitive optical amplification of an unknown quantum state is known to be a fundamentally noisy operation that inevitably adds noise to the amplified state [1 - 5]. However, this fundamental noise penalty in amplification can be…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…
Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example the discrete Fourier estimation that actually coincides with the operational phase of Noh, Fouge`res and Mandel is obtained for…
The standard model of classical Density Functional Theory for pair potentials consists of a hard-sphere functional plus a mean-field term accounting for long ranged attraction. However, most implementations using sophisticated Fundamental…
Gaussian states hold a fundamental place in quantum mechanics, quantum information, and quantum computing. Many subfields, including quantum simulation of continuous-variable systems, quantum chemistry, and quantum machine learning, rely on…
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…
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and…
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a…
State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…
We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help…