scholarly journals Experimental study of quantum coherence decomposition and trade-off relations in a tripartite system

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zhe Ding ◽  
Ran Liu ◽  
Chandrashekar Radhakrishnan ◽  
Wenchao Ma ◽  
Xinhua Peng ◽  
...  
Keyword(s):  
Experimental Study ◽  
Nuclear Spin ◽  
Quantum Coherence ◽  
Quantum Systems ◽  
Spin Systems ◽  
Quantum States ◽  
Product State ◽  
Trade Off ◽  
Global Coherence ◽  
Multipartite System

AbstractQuantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement. It can be distributed in a multipartite system in various ways—for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence), and exhibits a trade-off relation. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved nuclear spin systems using an NMR spectrometer. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous during the evolution. We find that the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.

scholarly journals Hallmarking quantum states: unified framework for coherence and correlations

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 109
Author(s):  
Gian Luca Giorgi ◽  
Roberta Zambrini
Keyword(s):  
Hilbert Space ◽  
Quantum Coherence ◽  
Quantum Correlations ◽  
The State ◽  
Quantum States ◽  
Tensor Structure ◽  
Unified Framework ◽  
Global Coherence ◽  
Simple Physical Interpretation ◽  
The Difference

Quantum coherence and distributed correlations among subparties are often considered as separate, although operationally linked to each other, properties of a quantum state. Here, we propose a measure able to quantify the contributions derived by both the tensor structure of the multipartite Hilbert space and the presence of coherence inside each of the subparties. Our results hold for any number of partitions of the Hilbert space. Within this unified framework, global coherence of the state is identified as the ingredient responsible for the presence of distributed quantum correlations, while local coherence also contributes to the quantumness of the state. A new quantifier, the "hookup", is introduced within such a framework. We also provide a simple physical interpretation, in terms of coherence, of the difference between total correlations and the sum of classical and quantum correlations obtained using relative-entropy-based quantifiers.

scholarly journals Matrix product state representations

2007 ◽  
Vol 7 (5&6) ◽  
pp. 401-430 ◽  
Author(s):  
D. Perez-Garcia ◽  
F. Verstraete ◽  
M.M. Wolf ◽  
J.I. Cirac
Keyword(s):  
Quantum Systems ◽  
Quantum States ◽  
Matrix Product ◽  
Canonical Forms ◽  
Product State ◽  
Matrix Product State ◽  
Translation Symmetry

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.

Dipole magnetic ordering in nuclear spin-spin systems

1975 ◽  
Vol 116 (7) ◽  
pp. 485 ◽  
Author(s):  
V.G. Pokazan'ev ◽  
G.V. Skrotskii ◽  
L.I. Yakub
Keyword(s):  
Nuclear Spin ◽  
Magnetic Ordering ◽  
Spin Systems

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.

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