Related papers: Quantum Description of Angles in the Plane
The interpretation of quantum mechanics continues to be debated, and quantum nonlocality accentuates the puzzle. Quantum interpretations can be classified broadly into two types: realist interpretations, which assert that quantum states…
We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
Bell suggested that a new perspective on quantum mechanics was needed. We propose a solution of the measurement problem based on a reconsideration of the nature of particles. The solution is presented with an idealized model involving…
We formulate the classical polarization theory for light by using entanglement analysis. We demonstrate a route to a systematic and consistent measure of ordinary light polarization that extends automatically to a new understanding of the…
Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
A characterization of N-partite states, based on K-way (K = 2 to N) negativities, is proposed. The K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences instead of K subsystems of the…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
Two qubits is the simplest system where the notions of separable and entangled states and entanglement witnesses first appear. We give a three dimensional geometric description of these notions. This description however carries no…
In this contribution we use the model of discrete spaces that we have put forward in former articles to give an interpretation to the phenomena of quantum entanglement and quantum states reduction that rests upon a new way of considering…
Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc. Here we introduce and…
The degree of polarization of a quantum state can be defined as its Hilbert-Schmidt distance to the set of unpolarized states. We demonstrate that the states optimizing this degree for a fixed average number of photons $\bar{N}$ present a…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
In this review we discuss intriguing properties of apparently classical optical fields, that go beyond purely classical context and allow us to speak about quantum characteristics of such fields and about their applications in quantum…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
I conjecture that only those states of light whose Wigner function is positive are real states, and give arguments suggesting that this is not a serious restriction. Hence it follows that the Wigner formalism in quantum optics is capable of…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…