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Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Automatic Word problem solving has always posed a great challenge for the NLP community. Usually a word problem is a narrative comprising of a few sentences and a question is asked about a quantity referred in the sentences. Solving word…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
Complex forms of quantum entanglement can arise in two qualitatively different ways; either between many qubits or between two particles with higher-than-qubit dimension. While the many-qubit frontier and the high-dimension frontier both…
We address the ultimate charge detection scheme with a quantum point contact. It is shown that a superposed input state is necessary to exploit the full sensitivity of a quantum point contact detector. The coherence of the input state…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…
We study the relationship between assumptions of state separability and both preparation and measurement contextuality, and the relationship of both of these to the frame problem, the problem of predicting what does not change in…
Time of arrival refers to the time a particle takes after emission to impinge upon a suitably idealized detector surface. Within quantum theory, no generally accepted solution exists so far for the corresponding probability distribution of…
Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the…
The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density…
Microscopically probing quantum many-body systems by resolving their constituent particles is essential for understanding quantum matter. In most physical systems, distinguishing individual particles, such as electrons in solids, or…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no…
There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…
We generalize the quantum CUSUM (QUSUM) algorithm for quickest change-point detection, analyzed in finite dimensions by Fanizza, Hirche, and Calsamiglia (Phys. Rev. Lett. 131, 020602, 2023), to infinite-dimensional quantum systems. Our…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The formalism of quantum estimation theory is applied to estimate the disorders in the positions of two membranes positioned in a driven cavity. We consider the coupled-cavities and the transmissive-regime models to obtain effective…