Related papers: Characterizing the intersection of QMA and coQMA
We introduce the Hopf algebra of quasi-symmetric functions with semigroup exponents generalizing the Hopf algebra QSym of quasi-symmetric functions. As a special case we obtain the Hopf algebra WCQSym of weak composition quasi-symmetric…
For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…
Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information…
In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between…
We discuss the finite temperature properties of the fermion correlation function near the fixed point theory of the nematic quantum critical point (QCP) of a metallic Fermi system. We show that though the fixed point theory is above its…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
Certain quantization problems are equivalent to the construction of morphisms from "quantum" to "classical" props. Once such a morphism is constructed, Hensel's lemma shows that it is in fact an isomorphism. This gives a new, simple proof…
This article demonstrates that the BFKL and CCFM equations, despite their different physical content, lead to equivalent results for any final-state observable at leading single-logarithmic order. A novel and fundamental element is the…
It is a common knowledge that the integer functions definable in simply typed lambda-calculus are exactly the extended polynomials. This is indeed the case when one interprets integers over the type (p->p)->p->p where p is a base type…
Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MM-QFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict…
The paper is in essence a survey of categories having $\phi$-weighted colimits for all the weights $\phi$ in some class $\Phi$. We introduce the class $\Phi^+$ of {\em $\Phi$-flat} weights which are those $\psi$ for which $\psi$-colimits…
This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. The key idea is to define two systems, one modelling…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
While in general there is no one-to-one correspondence between complex and quaternion quantum mechanics (QQM), there exists at least one version of QQM in which a {\em partial} set of {\em translations} may be made. We define these…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-K\"onig-Zeller operator $M_{q,n}$. These quantum Meyer-K\"onig-Zeller (MKZ) fractal functions employ $M_{q,n} f$ as the base function in the iterated…
The present paper is both a review on the Feynman problem, and an original research presentation on the relations between Fermionic theories and qubits theories, both regarded in the novel framework of operational probabilistic theories.…
We describe a joint cohomological framework for measurement-based quantum computation (MBQC) and the corresponding contextuality proofs. The central object in this framework is an element in the second cohomology group of the chain complex…