Related papers: Unknown Quantum States: The Quantum de Finetti Rep…
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
In this article, we propose to use the formalism of quantum mechanics to describe and explain the so-called "abnormal" behaviour of agents in certain decision or choice contexts. The basic idea is to postulate that the preferences of these…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor…
State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on…
The classical de Finetti Theorem classifies the $\mathrm{Sym}(\mathbb N)$-invariant probability measures on $[0,1]^{\mathbb N}$. More precisely it states that those invariant measures are combinations of measures of the form…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
The article explores challenges presented by revelations in physics and the questions they provoke concerning reality. It sheds light on the disparity between the indefinite nature of quantum reality and our perception of classical reality.…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key…
The notion of state vector is, in quantum mechanics, as central as it is problematic, as illustrates the wealth of publications about the sub- jects, including in particular the many attempts to obtain an acceptable interpretation of…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…