Related papers: Approximate traces on groups and the quantum compl…
In this series of papers, we develop the theory of a class of locally compact quantum groupoids, which is motivated by the purely algebraic notion of weak multiplier Hopf algebras. In this Part I, we provide motivation and formulate the…
Quantum information processing (QIP) requires thorough assessment of decoherence. Atoms or ions prepared for QIP often become addressed by radiation within schemes of alternating microwave-optical double resonance. A well-defined amount of…
Physical systems contain information which can be divided between classical and quantum information. Classical information is locally accessible and allows one to perform tasks such as physical work, while quantum information allows one to…
I offer a case that quantum query complexity still has loads of enticing and fundamental open problems -- from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial…
In multimodal learning, CLIP has been recognized as the \textit{de facto} method for learning a shared latent space across multiple modalities, placing similar representations close to each other and moving them away from dissimilar ones.…
We contribute to a recent research program which aims at revisiting the study of the complexity of word problems, a major area of research in combinatorial algebra, through the lens of the theory of computably enumerable equivalence…
Let $p$ be a prime number, $G$ be a finite $p$-group and $K$ be a field of characteristic $p$. The Modular Isomorphism Problem (MIP) asks whether the group algebra $KG$ determines the group $G$. Dealing with MIP, we investigated a question…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
While not yet in commercial existence, quantum computers have the ability to solve certain classes of problems that are not efficiently solvable on existing Turing Machine based (classical) computers. For quantum computers to be of use,…
Modal interpretations of quantum mechanics assign definite properties to physical systems and specify single-time joint probabilities of these properties. We show that a natural extension, applying to properties at several times, can be…
This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP,…
Closely related languages show linguistic similarities that allow speakers of one language to understand speakers of another language without having actively learned it. Mutual intelligibility varies in degree and is typically tested in…
Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
The correlation structure of multitime quantum processes - succinctly described by quantum combs - is an important resource for many quantum information protocols and control tasks. Inspired by approaches for quantum states, we introduce…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…
We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
Whether or not the Kronecker coefficients of the symmetric group count some set of combinatorial objects is a longstanding open question. In this work we show that a given Kronecker coefficient is proportional to the rank of a projector…
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the…