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We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…
How to find universal sets quantum gates (gates whose composition can form any othergate within a given range) is an important part of the development of quantum computation science that has been explored in the past with success. However,…
Bj\"orner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets (posets). They also introduced the notion of recursive atom ordering, and they proved that a…
We introduce several new set-theoretic axioms formulated in terms of coloring of ordinals by reals. We show that these axioms generalize the axioms considered by I.Juhasz, L.Soukup and Z.Szentmiklossy, and give a class of p.o.s including…
We summarise and discuss some of our previous results, which show that Bohr's theory of the one-electron atom may be derived from the theory underpinning Quantum ElectroDynamics (QED) or vice versa, and that General Relativity may also be…
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
In a recent paper [2], Chang et al. have proposed studying "Quantum $\mathbb{F}_{un}$": the $q \mapsto 1$ limit of Modal Quantum Theories over finite fields $\mathbb{F}_q$, motivated by the fact that such limit theories can be naturally…
We examine the "Guessing Secrets" problem arising in internet routing, in which the goal is to discover two or more objects from a known finite set. We propose a quantum algorithm using O(1) calls to an O(logN) oracle. This improves upon…
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
A secure quantum identification system combining a classical identification procedure and quantum key distribution is proposed. Each identification sequence is always used just once and new sequences are ``refuelled'' from a shared provably…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We show that a general linear transformation from one single photon qudit to another, the dimension of which can be either equal or unequal to that of the first one, can be implemented by linear optics. As an application of the scheme we…
Optical neural networks (ONNs) have been developed to enhance processing speed and energy efficiency in machine learning by leveraging optical devices for nonlinear activation and establishing connections among neurons. In this work, we…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…