scholarly journals Local and Non-Local Invasive Measurements on Two Quantum Spins Coupled via Nanomechanical Oscillations

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1078
Author(s):  
Dimitrios Maroulakos ◽  
Levan Chotorlishvili ◽  
Dominik Schulz ◽  
Jamal Berakdar
Keyword(s):  
Quantum Coherence ◽  
Indirect Measurement ◽  
Quantum Spin ◽  
Quantum States ◽  
Spin Interaction ◽  
First Case ◽  
Composite Quantum System ◽  
Local Quantum ◽  
Non Local ◽  
Quantum Spins

Symmetry plays the central role in the structure of quantum states of bipartite (or many-body) fermionic systems. Typically, symmetry leads to the phenomenon of quantum coherence and correlations (entanglement) inherent to quantum systems only. In the present work, we study the role of symmetry (i.e., quantum correlations) in invasive quantum measurements. We consider the influence of a direct or indirect measurement process on a composite quantum system. We derive explicit analytical expressions for the case of two quantum spins positioned on both sides of the quantum cantilever. The spins are coupled indirectly to each others via their interaction with a magnetic tip deposited on the cantilever. Two types of quantum witnesses can be considered, which quantify the invasiveness of a measurement on the systems’ quantum states: (i) A local quantum witness stands for the consequence on the quantum spin states of a measurement done on the cantilever, meaning we first perform a measurement on the cantilever, and subsequently a measurement on a spin. (ii) The non-local quantum witness signifies the response of one spin if a measurement is done on the other spin. In both cases the disturbance must involve the cantilever. However, in the first case, the spin-cantilever interaction is linear in the coupling constant Ω , where as in the second case, the spin-spin interaction is quadratic in Ω . For both cases, we find and discuss analytical results for the witness.

W-like states are not necessary for totally correct quantum anonymous leader election

2015 ◽  
Vol 15 (7&8) ◽  
pp. 677-684
Author(s):  
Alexander Norton
Keyword(s):  
Quantum State ◽  
Distributed Computation ◽  
Leader Election ◽  
Quantum States ◽  
W State ◽  
Correct Quantum ◽  
Local Quantum ◽  
Symmetric Quantum ◽  
Non Local ◽  
Entangled Quantum States

I show that $W$-like entangled quantum states are not a necessary quantum resource for totally correct anonymous leader election protocols. This is proven by defining a symmetric quantum state that is $n$-partite SLOCC inequivalent to the $W$ state, and then constructing a totally correct anonymous leader election protocol using this state. This result, which contradicts the previous necessity result of D'Hondt and Panangaden, furthers our understanding of how non-local quantum states can be used as a resource for distributed computation.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals Quantum Information in Neural Systems

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 773
Author(s):  
Danko D. Georgiev
Keyword(s):  
Quantum Entanglement ◽  
Quantum Coherence ◽  
Quantum Physics ◽  
Quantitative Measure ◽  
Quantum States ◽  
Quantum Evolution ◽  
Einstein Relation ◽  
Schmidt Decomposition ◽  
The Central Nervous System ◽  
The Individual

Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.

scholarly journals Local quantum uncertainty as a robust metric to characterize discord-like quantum correlations in subsets of the chromophores in photosynthetic light-harvesting complexes

2020 ◽  
Vol 66 (4 Jul-Aug) ◽  
pp. 525
Author(s):  
M. Chávez-Huerta ◽  
F. Rojas
Keyword(s):  
Quantum Coherence ◽  
Light Harvesting ◽  
Green Sulfur Bacteria ◽  
Quantum Correlations ◽  
Light Harvesting Complexes ◽  
Thermal Equilibrium State ◽  
Light Harvesting Complex ◽  
Quantum Uncertainty ◽  
Local Quantum Uncertainty ◽  
Local Quantum

Green sulfur bacteria is a photosynthetic organism whose light-harvesting complex accommodates a pigment-protein complex called Fenna-Matthews-Olson (FMO). The FMO complex sustains quantum coherence and quantum correlations between the electronic states of spatially separated pigment molecules as energy moves with nearly a 100% quantum efficiency to the reaction center. We present a method based on the quantum uncertainty associated to local measurements to quantify discord-like quantum correlations between two subsystems where one is a qubit and the other is a qudit. We implement the method by calculating local quantum uncertainty (LQU), concurrence, and coherence between subsystems of pure and mixed states represented by the eigenstates and by the thermal equilibrium state determined by the FMO Hamiltonian. Three partitions of the seven chromophores network define the subsystems: one chromophore with six chromophores, pairs of chromophores, and one chromophore with two chromophores. Implementation of the LQU approach allows us to characterize quantum correlations that had not been studied before, identify the most quantum correlated subsets of chromophores, and determine that, in the strongest associations of chromophores, the LQU is a monotonically increasing function of the coherence.

scholarly journals Renormalization and conformal invariance of non-local quantum electrodynamics

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Matthew Heydeman ◽  
Christian B. Jepsen ◽  
Ziming Ji ◽  
Amos Yarom
Keyword(s):  
Conformal Invariance ◽  
Quantum Electrodynamics ◽  
Local Quantum ◽  
Non Local

scholarly journals QUANTUM EVOLUTION IN SPACE–TIME FOAM

1999 ◽  
Vol 14 (26) ◽  
pp. 4079-4120 ◽  
Author(s):  
LUIS J. GARAY
Keyword(s):  
Quantum Coherence ◽  
Planck Scale ◽  
Space Time ◽  
Low Energy ◽  
Quantum Evolution ◽  
Minimum Length ◽  
Resolution Limit ◽  
Large Length ◽  
Non Local ◽  
Quantum Mechanical Systems

In this work, I review some aspects concerning the evolution of quantum low-energy fields in a foamlike space–time, with involved topology at the Planck scale but with a smooth metric structure at large length scales, as follows. Quantum gravitational fluctuations may induce a minimum length thus introducing an additional source of uncertainty in physics. The existence of this resolution limit casts doubts on the metric structure of space–time at the Planck scale and opens a doorway to nontrivial topologies, which may dominate Planck scale physics. This foamlike structure of space–time may show up in low-energy physics through loss of quantum coherence and mode-dependent energy shifts, for instance, which might be observable. Space–time foam introduces non-local interactions that can be modeled by a quantum bath, and low-energy fields evolve according to a master equation that displays such effects. Similar laws are also obtained for quantum mechanical systems evolving according to good real clocks, although the underlying Hamiltonian structure in this case establishes serious differences among both scenarios.

One-dimensional quantum spin heterojunction as a thermal switch

2016 ◽  
Vol 30 (07) ◽  
pp. 1650027
Author(s):  
Chuan-Jing Yang ◽  
Li-Hui Jin ◽  
Wei-Jiang Gong
Keyword(s):  
Thermal Transport ◽  
Structural Parameters ◽  
Finite Size ◽  
Quantum Spin ◽  
Spin Interaction ◽  
Heat Current ◽  
Spin Hamiltonian ◽  
One Dimensional ◽  
Thermal Switch ◽  
Wigner Transformation

We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.

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