Related papers: Quantum state collapse on a Riemann-Hilbert space …
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, we discuss…
With the example of a Stern-Gerlach measurement on a spin-1/2 atom, we show that a superposition of both paths may be observed compatibly with properties attributed to state collapse - for example, the singleness (or mutual exclusivity) of…
Quantum hashing is a promising generalization of the cryptographic hashing concept on the quantum domain. In this paper, we construct a quantum hash via a sequence of single-photon states and perform a proof-of-principle experiment using…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
This work introduces a novel model of quantum entities as unified, physically extended wavefields, forming the basis for a testable realist, holist framework for quantum measurement and collapse. Unlike interpretations that postulate hidden…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
The quantum measurement problem considered for measuring system (MS) model which consist of measured state S (particle), detector D and information processing device O. For spin chains and other O models the state evolution for MS…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this…