Related papers: The Two-State Vector Formalism
The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant {\Lambda}. We complete the program to canonically quantize the theory in the BF…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
We define a family of quantum invariants of closed oriented $3$-manifolds using spherical multi-fusion categories. The state sum nature of this invariant leads directly to $(2+1)$-dimensional topological quantum field theories…
Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…
In this article, we study the time-reversal properties of a generic Markovian stochastic field dynamics with Gaussian noise. We introduce a convenient functional geometric formalism that allows us to straightforwardly generalize known…
The standard formalism of quantum mechanics is extended to describe a total system including the reference system (RS), with respect to which the total system is described. The RS is assumed to be able to act as a measuring apparatus, with…
Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration…
We model vortex dynamics in a 2-dimensional Bose superfluid using the Thompson-Stamp (TS) equations of motion, which describes both the classical Hall-Vinen-Iordanskii (HVI) dynamical regime and the fully developed quantum regime, and the…
Recent authors have raised objections to the counterfactual interpretation of the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory (TSQT). I distinguish between two different readings of the ABL rule, counterfactual…
The questions we raise in this letter are as follows: What is the most general representation of a quantum state at a single point in time? Can we adapt the current formalisms to situations where the order of quantum operations is…
We consider the Feynman-Kitaev formalism applied to a spin chain described by the transverse field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete…
A recent result about measurability of a quantum state of a single quantum system is generalized to the case of a single pre- and post-selected quantum system described by a two-state vector. The protection required for such measurement is…
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These…
The general formalism of quantum mechanics for the description of statistical experiments is briefly reviewed, introducing in particular position and momentum observables as POVM characterized by their covariance properties with respect to…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the…
A general law is presented for (composite) quantum systems which directly describes the time evolution of quantum states (with one or both components) through an arbitrary noisy quantum channel. It is shown that the time evolution of all…
We celebrate this year hundred years of quantum mechanics but there is still no consensus regarding its interpretation and limitations. In this article we advocate the statistical contextual interpretation which is free of paradoxes. State…