相关论文: Symplectic Cuts and Projection Quantization
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be…
Taking projections of high-dimensional data is a common analytical and visualisation technique in statistics for working with high-dimensional problems. Sectioning, or slicing, through high dimensions is less common, but can be useful for…
Tangential computed tomography (TCT) is a useful tool for imaging the large-diameter samples, such as oil pipelines and rockets. However, TCT projections are truncated along the detector direction, resulting in degraded slices with radial…
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system, or has to artificially break certain…
We introduce the concept of selective quantum state tomography or SQST, a tomographic scheme that enables a user to estimate arbitrary elements of an unknown quantum state using a fixed measurement record. We demonstrate how this may be…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
A midi-superspace model is a field theory obtained by symmetry reduction of a parent gravitational theory. Such models have proven useful for exploring the classical and quantum dynamics of the gravitational field. I present 3 recent…
Quantization has proven effective in high-resolution and large-scale simulations, which benefit from bit-level memory saving. However, identifying a quantization scheme that meets the requirement of both precision and memory efficiency…
We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, intrinsic losses as well as the positions of an arbitrary number of…
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…
In this paper, we present a characterization of metric projection in CAT(0) spaces by using the concept of quasilinearization. Furthermore, some basic properties of matric projection are investigated.
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess…
A G-equivariant spin^c structure on a manifold gives rise to a virtual representation of the group G, called the spin^c quantization of the manifold. We present a cutting construction for S^1-equivariant spin^c manifolds, and show that the…
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results…
Quantum Telescope is a recent idea aimed at beating the diffraction limit of spaceborne telescopes and possibly also other distant target imaging systems. There is no agreement yet on the best setup of such devices, but some configurations…
Finite frame quantization is a discrete version of the coherent state quantization. In the case of a quantum system with finite-dimensional Hilbert space, the finite frame quantization allows us to associate a linear operator to each…
How can we use a quantum computer to detect the entanglement structure of a quantum state? Bouland et al. (2024) recently provided an algorithm that, given multiple input copies of the state, finds the "hidden cuts"-partitions into fully…