Related papers: Time Reversal and n-qubit Canonical Decompositions
Time reversal ($T$) and space inversion are symmetries of our universe in the low-energy limit. Fundamental theorems relate their corresponding quantum numbers to the spin for elementary particles: $\hat{T}^2=(\hat{P}\hat{T})^2=-1$ for…
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…
We argue that Hopf-algebra deformations of symmetries -- as encountered in non-commutative models of quantum spacetime -- carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite…
The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schr\"odinger…
In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically,…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We experimentally demonstrate that it is impossible to simulate quantum bipartite correlations with a deterministic universal Turing machine. Our approach is based on the Normalized Information Distance (NID) that allows the comparison of…
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…
In this work we initiate a systematic investigation of the spin of a composite system in an arbitrary reference frame in QCD. After a brief review of the difficulties one encounters in equal-time quantization, we turn to light-front…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We…
Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
In this study, we propose a spin-star model for spin-(1/2) particles in order to examine the coherence dynamics of a quantum neural network (QNN) unit. Since quantum computing paradigm promises advantages over their classical counterparts,…
We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $\alpha$. Using the strong disorder renormalization group (SDRG) technique, we find by…