Maximum weight vectors possess minimal uncertainty

Delbourgo, R.; Fox, Jonathan

doi:10.1088/0305-4470/10/12/004

Cited by 48 publications

(33 citation statements)

References 2 publications

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“…As mentioned earlier, a pure quantum state |ψ is defined to be generalized entangled (general- [35,36], so that, similar to the familiar harmonic-oscillator ones, they may be regarded in some sense as closest to "classical" states.…”

Section: A Relative Purity For Faithfully Represented Lie Algebrasmentioning

confidence: 99%

Nature and measure of entanglement in quantum phase transitions

et al. 2004

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Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum state relative to an observable set. For the algebra of local observables on multi-qubit systems, the resulting local purity measure is equivalent to a recently introduced global entanglement measure [Meyer and Wallach, J. Math. Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of Lie-algebraic purity is exploited to identify and characterize the quantum phase transitions present in two exactly solvable models: the Lipkin-Meshkov-Glick model, and the spin-1/2 anisotropic XY model in a transverse magnetic field. For the latter, we argue that a natural fermionic observable-set arising after the Jordan-Wigner transformation, better characterizes the transition than alternative measures based on qubits. This illustrates the usefulness of going beyond the standard subsystem-based framework while providing a global disorder parameter for this model. Our results show how generalized entanglement leads to useful tools for distinguishing between the ordered and disordered phases in the case of broken symmetry quantum phase transitions. Additional implications and possible extensions of concepts to other systems of interest in condensed matter physics are also discussed.

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Section: A Relative Purity For Faithfully Represented Lie Algebrasmentioning

confidence: 99%

Nature and measure of entanglement in quantum phase transitions

et al. 2004

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“…Lemma 2 (Delbourgo and Fox [8]). The minimum of the uncertainty ( T ) 2 ≡ T 2 − T 2 is obtained for coherent states…”

Section: Proof Of the Main Resultsmentioning

confidence: 99%

Monte Carlo Study of Charge Injection Transistors (CHINTs)

Akeyoshi¹,

Maezawa²,

Tomizawa³

et al. 1993

Jpn. J. Appl. Phys.

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“…Nevertheless, one could study the evolution of such a system with the constraints analogous to (23). The constraint manifold of such a system with a Lie dynamical algebra g should coincide with the manifold of the corresponding g-generalized coherent states [25][26][27].…”

Section: B Quantum Constrained System and The Classical Oscillatormentioning

confidence: 99%

System of classical nonlinear oscillators as a coarse-grained quantum system

2011

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Constrained Hamiltonian dynamics of a quantum system of nonlinear oscillators is used to provide the mathematical formulation of a coarse-grained description of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of the corresponding classical system on a sufficiently large scale.

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Maximum weight vectors possess minimal uncertainty

Cited by 48 publications

References 2 publications

Nature and measure of entanglement in quantum phase transitions

Nature and measure of entanglement in quantum phase transitions

Monte Carlo Study of Charge Injection Transistors (CHINTs)

System of classical nonlinear oscillators as a coarse-grained quantum system

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