相关论文: Limitations on quantum dimensionality reduction

In this work, we use the JKO scheme to approximate a general class of diffusion problems generated by Darcy's law. Although the scheme is now classical, if the energy density is spatially inhomogeneous or irregular, many standard methods…

In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall…

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system; e.g., a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels,…

We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize…

We consider the minimum distance projection in the $L_2$-norm from an arbitrary point in an $n$-dimensional, Euclidian space onto the canonical simplex. It is shown that this problem reduces to a univariate problem that can be solved by a…

The calculation of Euclidean distance between points is generalized to one-dimensional objects such as strings or polymers. Necessary and sufficient conditions for the minimal transformation between two polymer configurations are derived.…

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an…

We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for both finite-dimensional and continuous-variable quantum-to-classical systems with limited classical common…

We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…

Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…

We introduce a high-dimensional quantum encoding based on coherent mode-dependent single-photon subtraction from multimode squeezed states. This encoding can be seen as a generalization to the case of non-zero squeezing of the standard…

We discuss no-dimensional (approximate) versions of Carath\'eodory's and Helly's theorems. Our goal is to draw attention to open problems and potential applications related to these results. We survey recent progress and pose several…

We adopt a framework where quantum-gravity's dynamical dimensional reduction of spacetime at short distances is described in terms of modified dispersion relations. We observe that by subjecting such models to a momentum-space…

Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…

It is shown that the local coupling of a higher dimensional graviton to a closed degenerate two-form produces dimensional reduction by spontaneous breakdown of extra-dimensional translational symmetry. Four dimensional Poincar\'e invariance…

Compressed sensing is the art of reconstructing structured $n$-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytic reconstruction guarantees support this credo. The strongest among them…

In this paper we present a theory of reduction of quantum systems in the presence of symmetries and constraints. The language used is that of Lie--Jordan Banach algebras, which are discussed in some detail together with spectrum properties…

The present paper studies an operator norm that captures the distinguishability of quantum strategies in the same sense that the trace norm captures the distinguishability of quantum states or the diamond norm captures the…

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…

Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…