scholarly journals Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1292
Author(s):  
Florio M. Ciaglia ◽  
Fabio Di Di Cosmo ◽  
Alberto Ibort ◽  
Giuseppe Marmo
Keyword(s):  
Composite System ◽  
Classical System ◽  
Quantum Systems ◽  
Entangled State ◽  
Countable Number ◽  
Unitary Evolution ◽  
Von Neumann ◽  
New Family ◽  
Abelian Von Neumann Algebra ◽  
Totally Disconnected

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.

scholarly journals Koopman wavefunctions and classical–quantum correlation dynamics

2019 ◽  
Vol 475 (2229) ◽  
pp. 20180879 ◽  
Author(s):  
Denys I. Bondar ◽  
François Gay-Balmaz ◽  
Cesare Tronci
Keyword(s):  
Hamiltonian Structure ◽  
Classical System ◽  
Solvable Model ◽  
Infinite Family ◽  
Dynamical Theory ◽  
Quantum Systems ◽  
Von Neumann ◽  
Proposed Model ◽  
Exactly Solvable ◽  
Classical Quantum

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman–von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical–quantum coupling. The proposed model not only describes the influence of a classical system onto a quantum one, but also the reverse effect—the quantum backreaction. These interactions are described by a new Hamiltonian wave equation overcoming shortcomings of currently employed models. For example, the density matrix of the quantum subsystem is always positive definite. While the Liouville density of the classical subsystem is generally allowed to be unsigned, its sign is shown to be preserved in time for a specific infinite family of hybrid classical–quantum systems. The proposed description is illustrated and compared with previous theories using the exactly solvable model of a degenerate two-level quantum system coupled to a classical harmonic oscillator.

scholarly journals ON THE EQUIVALENCE OF THE CH AND CHSH INEQUALITIES FOR TWO THREE-LEVEL SYSTEMS

2003 ◽  
Vol 01 (01) ◽  
pp. 115-133 ◽  
Author(s):  
JOSÉ L. CERECEDA
Keyword(s):  
Quantum Efficiency ◽  
Quantum Systems ◽  
Optimal Choice ◽  
Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Realistic Description ◽  
Von Neumann Measurements ◽  
Chsh Inequalities

In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [Phys. Rev. A65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acin et al. [Phys. Rev. A65, 052325 (2002)]. This equivalence, however, breaks down when one takes into account the less-than-perfect quantum efficiency of detectors. Indeed, for the noiseless case, the threshold quantum efficiency above which there is no local and realistic description of the experiment for the optimal choice of measurements is found to be [Formula: see text] for the CH inequality, whereas it is equal to [Formula: see text] for the CHSH inequality.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

scholarly journals Simulating molecules on a cloud-based 5-qubit IBM-Q universal quantum computer

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
S. Leontica ◽  
F. Tennie ◽  
T. Farrow
Keyword(s):  
Quantum System ◽  
Energy Transport ◽  
Quantum Computer ◽  
Complex Molecule ◽  
Dissipative System ◽  
Quantum Simulation ◽  
Quantum Systems ◽  
Molecular Structures ◽  
Unitary Evolution ◽  
Universal Quantum

AbstractSimulating the behaviour of complex quantum systems is impossible on classical supercomputers due to the exponential scaling of the number of quantum states with the number of particles in the simulated system. Quantum computers aim to break through this limit by using one quantum system to simulate another quantum system. Although in their infancy, they are a promising tool for applied fields seeking to simulate quantum interactions in complex atomic and molecular structures. Here, we show an efficient technique for transpiling the unitary evolution of quantum systems into the language of universal quantum computation using the IBM quantum computer and show that it is a viable tool for compiling near-term quantum simulation algorithms. We develop code that decomposes arbitrary 3-qubit gates and implement it in a quantum simulation first for a linear ordered chain to highlight the generality of the approach, and second, for a complex molecule. We choose the Fenna-Matthews-Olsen (FMO) photosynthetic protein because it has a well characterised Hamiltonian and presents a complex dissipative system coupled to a noisy environment that helps to improve the efficiency of energy transport. The method can be implemented in a broad range of molecular and other simulation settings.

Bell inequality for quNits with binary measurements

2003 ◽  
Vol 3 (2) ◽  
pp. 157-164
Author(s):  
H. Bechmann-Pasquinucci ◽  
N. Gisin
Keyword(s):  
Quantum Cryptography ◽  
Bell Inequality ◽  
The Other ◽  
Entangled State ◽  
Maximally Entangled State ◽  
Von Neumann ◽  
Chsh Inequality ◽  
Intermediate States ◽  
Von Neumann Measurements

We present a generalized Bell inequality for two entangled quNits. On one quNit the choice is between two standard von Neumann measurements, whereas for the other quNit there are N^2 different binary measurements. These binary measurements are related to the intermediate states known from eavesdropping in quantum cryptography. The maximum violation by \sqrt{N} is reached for the maximally entangled state. Moreover, for N=2 it coincides with the familiar CHSH-inequality.

Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras

2014 ◽  
Vol 17 (04) ◽  
pp. 1450028 ◽  
Author(s):  
Marek Miller ◽  
Robert Olkiewicz
Keyword(s):  
Quantum Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Mixed States ◽  
Von Neumann ◽  
C Algebras ◽  
Necessary And Sufficient

The Horodeckis necessary and sufficient condition of separability of mixed states is generalized to arbitrary composite quantum systems.

ENCRYPTION OF QUANTUM INFORMATION

2003 ◽  
Vol 14 (05) ◽  
pp. 741-755 ◽  
Author(s):  
JAN BOUDA ◽  
VLADIMÍ R. BUŽEK
Keyword(s):  
Quantum Information ◽  
Quantum Channel ◽  
Composite System ◽  
Quantum Systems ◽  
Noisy Channel ◽  
Classical Description ◽  
Quantum Analogue ◽  
Known Plaintext Attack

We study in detail the problem of encryption of quantum information. We present an attack on a private quantum channel (PQC) which applies when partial classical description of a ciphertext is known (the so-called known-ciphertext attack) and we show how this situation can be avoided. The quantum analogue of the known plaintext attack is also discussed. We determine how correlations between quantum systems can be encrypted and we conclude that two PQCs on the subsystems form a PQC on the whole composite system. Finally, some applications of the PQC are suggested and a security of a noisy channel is discussed.

scholarly journals Equilibrium Wigner Function for Fermions and Bosons in the Case of a General Energy Dispersion Relation

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1023
Author(s):  
Vito Dario Camiola ◽  
Liliana Luca ◽  
Vittorio Romano
Keyword(s):  
Wigner Function ◽  
Natural Generalization ◽  
Bloch Equation ◽  
Equilibrium Density ◽  
Diagonal Form ◽  
Energy Dispersion ◽  
Unitary Evolution ◽  
Von Neumann ◽  
General Energy

The approach based on the Wigner function is considered as a viable model of quantum transport which allows, in analogy with the semiclassical Boltzmann equation, to restore a description in the phase-space. A crucial point is the determination of the Wigner function at the equilibrium which stems from the equilibrium density function. The latter is obtained by a constrained maximization of the entropy whose formulation in a quantum context is a controversial issue. The standard expression due to Von Neumann, although it looks a natural generalization of the classical Boltzmann one, presents two important drawbacks: it is conserved under unitary evolution time operators, and therefore cannot take into account irreversibility; it does not include neither the Bose nor the Fermi statistics. Recently a diagonal form of the quantum entropy, which incorporates also the correct statistics, has been proposed in Snoke et al. (2012) and Polkovnikov (2011). Here, by adopting such a form of entropy, with an approach based on the Bloch equation, the general condition that must be satisfied by the equilibrium Wigner function is obtained for general energy dispersion relations, both for fermions and bosons. Exact solutions are found in particular cases. They represent a modulation of the solution in the non degenerate situation.

scholarly journals IBM Q Experience as a versatile experimental testbed for simulating open quantum systems

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Guillermo García-Pérez ◽  
Matteo A. C. Rossi ◽  
Sabrina Maniscalco
Keyword(s):  
Quantum Electrodynamics ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Cavity Quantum Electrodynamics ◽  
Quantum Systems ◽  
Entangled State ◽  
Specific Class ◽  
Linear Optics ◽  
Open Quantum ◽  
State Generation

AbstractThe advent of noisy intermediate-scale quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here, we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory. During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from nuclear magnetic resonance (NMR) to cavity quantum electrodynamics. Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class. Our main result is to prove the great versatility of the IBM Q Experience processors. Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions. Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects. All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online.

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