Related papers: Tomographic Reconstruction of Quantum Metrics
In bosonic quantum metrology, the estimate of a loss parameter is typically performed by means of pure states, such as coherent, squeezed or entangled states, while mixed thermal probes are discarded for their inferior performance. Here we…
We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the…
We propose a tomographic approach to study quantum nonlocality in continuous variable quantum systems. On one hand we derive a Bell-like inequality for measured tomograms. On the other hand, we introduce pseudospin operators whose…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
The advantage that quantum systems provide for certain quantum information processing tasks over their classical counterparts can be quantified within the general framework of resource theories. Certain distance functions between quantum…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Based on the fundamental principles of Relativistic Quantum Mechanics, we give a rigorous, but completely elementary, proof of the relation between fundamental observables of a statistical system when measured relatively to two inertial…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown…
Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum field theories (QFTs). They have been used to solve…
Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…