scholarly journals Schwinger’s picture of quantum mechanics IV: Composition and independence

2020 ◽  
Vol 17 (04) ◽  
pp. 2050058 ◽  
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo
Keyword(s):  
Quantum Mechanics ◽  
Entangled State ◽  
Total System ◽  
Free Products ◽  
Algebraic Description ◽  
Free Independence

The groupoid description of Schwinger’s picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger’s groupoid of the system. The groupoid picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoid formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic “non-separability” associated to the impossibility of identifying the entangled particles as subsystems of the total system.

Properties of implication in effect algebras

2021 ◽  
Vol 71 (3) ◽  
pp. 523-534
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
State Space ◽  
Effect Algebra ◽  
Modus Ponens ◽  
Effect Algebras ◽  
Algebraic Semantics ◽  
Deductive Systems ◽  
Algebraic Description ◽  
Residuated Poset

Abstract Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serve as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, more precisely as an algebraic semantics of these logics. Because every productive logic is equipped with implication, we introduce here such a concept and demonstrate its properties. In particular, we show that this implication is connected with conjunction via a certain “unsharp” residuation which is formulated on the basis of a strict unsharp residuated poset. Though this structure is rather complicated, it can be converted back into an effect algebra and hence it is sound. Further, we study the Modus Ponens rule for this implication by means of so-called deductive systems and finally we study the contraposition law.

scholarly journals ENTANGLEMENT QUANTISTICO

2020 ◽  
Author(s):  
Alberto Rimini
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
First Principles ◽  
Measurement Problem ◽  
Entangled State ◽  
Uncertainty Relations ◽  
Entanglement State ◽  
State Uncertainty ◽  
Einstein Podolsky Rosen

This extended note deals with a pedagogical description of the entangled state of two particles, starting from first principles. After some general remarks about quantum mechanics and physical theories, the single particle case is discussed by defining state, uncertainty relations and wave function in the state space. The system of two particles is then considered, with its possible states, starting from the original papers by Einstein Podolsky Rosen and by Schroedinger. The quantum measurement problem is then introduced, together with its role in the entanglement state. Finally the orthodox solution and the relevant conclusions are drawn.

scholarly journals Proposal to Test a Transient Deviation from Quantum Mechanics’ Predictions for Bell’s Experiment

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1589
Author(s):  
Alejandro Andrés Hnilo ◽  
Monica Beatriz Agüero ◽  
Marcelo Gregorio Kovalsky
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Quantum Correlations ◽  
Entangled State ◽  
Particle Detection ◽  
Specific Test ◽  
Nonlinear Operators ◽  
Model Following ◽  
Proposed Model ◽  
Faster Than Light

Quantum mechanics predicts correlations between measurements performed in distant regions of a spatially spread entangled state to be higher than allowed by intuitive concepts of Locality and Realism. These high correlations forbid the use of nonlinear operators of evolution (which would be desirable for several reasons), for they may allow faster-than-light signaling. As a way out of this situation, it has been hypothesized that the high quantum correlations develop only after a time longer than L/c has elapsed (where L is the spread of the entangled state and c is the velocity of light). In shorter times, correlations compatible with Locality and Realism would be observed instead. A simple hidden variables model following this hypothesis is described. It is based on a modified Wheeler–Feynman theory of radiation. This hypothesis has not been disproved by any of the experiments performed to date. A test achievable with accessible means is proposed and described. It involves a pulsed source of entangled states and stroboscopic record of particle detection during the pulses. Data recorded in similar but incomplete optical experiments are analyzed, and found consistent with the proposed model. However, it is not claimed, in any sense, that the hypothesis has been validated. On the contrary, it is stressed that a complete, specific test is absolutely needed.

Connections between Weyl geometry, quantum potential and quantum entanglement

2021 ◽  
Author(s):  
Shi-Dong Liang ◽  
Wenjing Huang
Keyword(s):  
Quantum Mechanics ◽  
Scalar Curvature ◽  
Quantum Entanglement ◽  
Quantum Potential ◽  
Entangled State ◽  
Dimensional System ◽  
Weyl Geometry ◽  
3D Space ◽  
Potential Applications ◽  
Weyl Scalar

The Weyl geometry promises potential applications in gravity and quantum mechanics. We study the relationships between the Weyl geometry, quantum entropy and quantum entanglement based on the Weyl geometry endowing the Euclidean metric. We give the formulation of the Weyl Ricci curvature and Weyl scalar curvature in the n-dimensional system. The Weyl scalar field plays a bridge role to connect the Weyl scalar curvature, quantum potential and quantum entanglement. We also give the Einstein–Weyl tensor and the generalized field equation in 3D vacuum case, which reveals the relationship between Weyl geometry and quantum potential. Particularly, we find that the correspondence between the Weyl scalar curvature and quantum potential is dimension-dependent and works only for the 3D space, which reveals a clue to quantize gravity and an understanding why our space must be 3D if quantum gravity is compatible with quantum mechanics. We analyze numerically a typical example of two orthogonal oscillators to reveal the relationships between the Weyl scalar curvature, quantum potential and quantum entanglement based on this formulation. We find that the Weyl scalar curvature shows a negative dip peak for separate state but becomes a positive peak for the entangled state near original point region, which can be regarded as a geometric signal to detect quantum entanglement.

Quantum entangling or disentangling by complex integration transformation

2020 ◽  
Vol 35 (25) ◽  
pp. 2050211
Author(s):  
Chun-Zao Zhang ◽  
Jian-Ming Du ◽  
Hong-Yi Fan
Keyword(s):  
Quantum Mechanics ◽  
Complex Space ◽  
Entangled State ◽  
Entangled State Representation ◽  
State Representation ◽  
Operator Ordering ◽  
Complex Integration

We find some new integration transformations in complex space, which plays the role of entangling or disentangling in quantum mechanics. Their applications in operator ordering are presented. We employ the entangled state representation and the method of integration within ordered product of operators (IWOP) to find them.

ENTANGLED STATE REPRESENTATION FOR A PARTICLE ON A CIRCLE STUDIED IN TERMS OF BOSONIC OPERATOR REALIZATION OF ANGULAR MOMENTUM

2006 ◽  
Vol 21 (27) ◽  
pp. 2079-2085 ◽  
Author(s):  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Entangled States ◽  
Entangled State ◽  
Entangled State Representation ◽  
Phase Operator ◽  
State Representation ◽  
New Formalism ◽  
Bosonic Operator ◽  
Operator Realization

By introducing the bosonic operator realization of angular momentum, we establish the entangled state representation for describing quantum mechanics of a particle on a circle. The phase operator, the angular momentum eigenstates, the lowering and ascending operators for angular momentum are all well expressed in the bosonic realization with the aid of appropriate entangled states, i.e. we establish a new formalism for the quantum mechanics of a particle on a circle.

scholarly journals Nonlocal single particle steering generated through single particle entanglement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
L. M. Arévalo Aguilar
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Single Particle ◽  
Thought Experiment ◽  
Nonlocal Effect ◽  
Historical Event ◽  
Entangled State ◽  
Nonlocal Effects ◽  
Action At A Distance

AbstractIn 1927, at the Solvay conference, Einstein posed a thought experiment with the primary intention of showing the incompleteness of quantum mechanics; to prove it, he employed the instantaneous nonlocal effects caused by the collapse of the wavefunction of a single particle—the spooky action at a distance–, when a measurement is done. This historical event preceded the well-know Einstein–Podolsk–Rosen criticism over the incompleteness of quantum mechanics. Here, by using the Stern–Gerlach experiment, we demonstrate how the instantaneous nonlocal feature of the collapse of the wavefunction together with the single-particle entanglement can be used to produce the nonlocal effect of steering, i.e. the single-particle steering. In the steering process Bob gets a quantum state depending on which observable Alice decides to measure. To accomplish this, we fully exploit the spreading (over large distances) of the entangled wavefunction of the single-particle. In particular, we demonstrate that the nonlocality of the single-particle entangled state allows the particle to “know” about the kind of detector Alice is using to steer Bob’s state. Therefore, notwithstanding strong counterarguments, we prove that the single-particle entanglement gives rise to truly nonlocal effects at two faraway places. This opens the possibility of using the single-particle entanglement for implementing truly nonlocal task.

scholarly journals Large violations in Kochen Specker contextuality and their applications

2021 ◽  
Author(s):  
Ravishankar Ramanathan ◽  
Yuan Liu ◽  
Pawel Horodecki
Keyword(s):  
Quantum Mechanics ◽  
Present State ◽  
Hilbert Spaces ◽  
Independent Interest ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Technical Result ◽  
Orthogonal Representation ◽  
State Dependent ◽  
Minimum Dimension

Abstract It is of interest to study how contextual quantum mechanics is, in terms of the violation of Kochen Specker state-independent and state-dependent non-contextuality inequalities. We present state-independent non-contextuality inequalities with large violations, in particular, we exploit a connection between Kochen-Specker proofs and pseudo-telepathy games to show KS proofs in Hilbert spaces of dimension $d \geq 2^{17}$ with the ratio of quantum value to classical bias being $O(\sqrt{d}/\log d)$. We study the properties of this KS set and show applications of the large violation. It has been recently shown that Kochen-Specker proofs always consist of substructures of state-dependent contextuality proofs called $01$-gadgets or bugs. We show a one-to-one connection between $01$-gadgets in $\mathbb{C}^d$ and Hardy paradoxes for the maximally entangled state in $\mathbb{C}^d \otimes \mathbb{C}^d$. We use this connection to construct large violation $01$-gadgets between arbitrary vectors in $\mathbb{C}^d$, as well as novel Hardy paradoxes for the maximally entangled state in $\mathbb{C}^d \otimes \mathbb{C}^d$, and give applications of these constructions. As a technical result, we show that the minimum dimension of the faithful orthogonal representation of a graph in $\mathbb{R}^d$ is not a graph monotone, a result that may be of independent interest.

Sign in / Sign up

Export Citation Format

Share Document