A Logical Basis for Quantum Evolution and Entanglement

Unitary bounds and controllability of quantum evolution in NMR spectroscopy

Molecular Physics ◽

10.1080/002689799164171 ◽

1999 ◽

Vol 96 (12) ◽

pp. 1739-1744 ◽

Cited By ~ 3

Author(s):

T. S. UNTIDT, S. J. GLASER, C. GRIESIN

Keyword(s):

Nmr Spectroscopy ◽

Quantum Evolution

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Eternal adiabaticity in quantum evolution

Physical Review A ◽

10.1103/physreva.103.032214 ◽

2021 ◽

Vol 103 (3) ◽

Author(s):

Daniel Burgarth ◽

Paolo Facchi ◽

Hiromichi Nakazato ◽

Saverio Pascazio ◽

Kazuya Yuasa

Keyword(s):

Quantum Evolution

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Quantum Information in Neural Systems

Symmetry ◽

10.3390/sym13050773 ◽

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.

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Noise-Assisted Discord-Like Correlations in Light-Harvesting Photosynthetic Complexes

Quantum Reports ◽

10.3390/quantum3020016 ◽

2021 ◽

Vol 3 (2) ◽

pp. 262-271

Author(s):

Pablo Reséndiz-Vázquez ◽

Ricardo Román-Ancheyta ◽

Roberto León-Montiel

Keyword(s):

Potential Role ◽

Energy Transport ◽

Light Harvesting ◽

Quantum Correlations ◽

Transport Processes ◽

Quantum Evolution ◽

Light Harvesting Complexes ◽

Transport Efficiency ◽

Photovoltaic Materials ◽

Photosynthetic Complexes

Transport phenomena in photosynthetic systems have attracted a great deal of attention due to their potential role in devising novel photovoltaic materials. In particular, energy transport in light-harvesting complexes is considered quite efficient due to the balance between coherent quantum evolution and decoherence, a phenomenon coined Environment-Assisted Quantum Transport (ENAQT). Although this effect has been extensively studied, its behavior is typically described in terms of the decoherence’s strength, namely weak, moderate or strong. Here, we study the ENAQT in terms of quantum correlations that go beyond entanglement. Using a subsystem of the Fenna–Matthews–Olson complex, we find that discord-like correlations maximize when the subsystem’s transport efficiency increases, while the entanglement between sites vanishes. Our results suggest that quantum discord is a manifestation of the ENAQT and highlight the importance of beyond-entanglement correlations in photosynthetic energy transport processes.

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Probability distributions of continuous measurement results for two noncommuting variables and postselected quantum evolution

Physical Review A ◽

10.1103/physreva.100.062109 ◽

2019 ◽

Vol 100 (6) ◽

Cited By ~ 1

Author(s):

A. Franquet ◽

Yuli V. Nazarov

Keyword(s):

Continuous Measurement ◽

Probability Distributions ◽

Quantum Evolution ◽

Measurement Results

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Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions

Communications in Mathematical Physics ◽

10.1007/s00220-019-03594-2 ◽

2019 ◽

Vol 374 (2) ◽

pp. 823-871 ◽

Cited By ~ 5

Author(s):

Simon Becker ◽

Nilanjana Datta

Keyword(s):

Convergence Rates ◽

Lipschitz Continuity ◽

Open Quantum Systems ◽

High Energy ◽

Quantum Systems ◽

Quantum Evolution ◽

Infinite Dimensions ◽

Quantum Brownian Motion ◽

Infinite Dimensional ◽

Energy Constrained

Abstract By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl’s law.

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