Related papers: A Finite de Finetti Theorem for Infinite-Dimension…
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some…
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
Symmetry plays an important role in the field of quantum mechanics. In this paper, we consider a subclass of symmetric quantum states in the multipartite system $N^{\otimes d}$, namely, the completely symmetric states, which are invariant…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…
The separability and entanglement of quantum mixed states in $\Cb^2 \otimes \Cb^3 \otimes \Cb^N$ composite quantum systems are investigated. It is shown that all quantum states $\rho$ with positive partial transposes and rank $r(\rho)\leq…
In this paper, by providing a class of coherence measures in finite dimensional systems, a sufficient and necessary condition for the existence of coherence transformations that convert one probability distribution of any pure states into…
Completeness is proved for some subsystems of a system of coherent states. The linear dependence of states is investigated for the von Neumann type subsystems. A detailed study is made of the case when a regular lattice on the complex…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
In this work, we revisit the problem of finding an admissible region of fidelities obtained after an application of an arbitrary $1 \rightarrow N$ universal quantum cloner which has been recently solved in [A. Kay et al., Quant. Inf. Comput…
We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Markov categories have recently emerged as a powerful high-level framework for probability theory and theoretical statistics. Here we study a quantum version of this concept, called involutive Markov categories. These are equivalent to…
In this paper we consider theories in which reality is described by some underlying variables. Each value these variables can take represents an ontic state (a particular state of reality). The preparation of a quantum state corresponds to…