Frobenius-norm-based measures of quantum coherence and asymmetry

Yao, Yao; Dong, Guohui; Xing, Xiao; Sun, Changhua

doi:10.1038/srep32010

Cited by 47 publications

(43 citation statements)

References 84 publications

(217 reference statements)

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“…In fact, there exists a simple direct relationship between them C P (ρ) = (d − 1)C F (ρ), which indicates that the basis-independent quantity C F (ρ) can also be viewed as a renormalized measure of the maximal coherence contained in a given state. Intriguingly, we found that for d = 2 and 3, the formula of C P (ρ) coincides with that of O d , due to an equivalent expression of C F (ρ) [29] C F (ρ) = 1 2(d − 1)…”

Section: Discussionmentioning

confidence: 62%

Maximal coherence in a generic basis

Yao

Dong

et al. 2016

Phys. Rev. A

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Since quantum coherence is an undoubted characteristic trait of quantum physics, the quantification and application of quantum coherence has been one of the long-standing central topics in quantum information science. Within the framework of a resource theory of quantum coherence proposed recently, a fiducial basis should be pre-selected for characterizing the quantum coherence in specific circumstances, namely, the quantum coherence is a basis-dependent quantity. Therefore, a natural question is raised: what are the maximum and minimum coherences contained in a certain quantum state with respect to a generic basis? While the minimum case is trivial, it is not so intuitive to verify in which basis the quantum coherence is maximal. Based on the coherence measure of relative entropy, we indicate the particular basis in which the quantum coherence is maximal for a given state, where the Fourier matrix (or more generally, complex Hadamard matrices) plays a critical role in determining the basis. Intriguingly, though we can prove that the basis associated with the Fourier matrix is a stationary point for optimizing the l 1 norm of coherence, numerical simulation shows that it is not a global optimal choice.

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Section: Discussionmentioning

confidence: 62%

Maximal coherence in a generic basis

Yao

Dong

et al. 2016

Phys. Rev. A

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“…Recently, resource theory of asymmetry or reference frame has emerged which treats individual formulations of coherence measures as special cases [18][19][20][21][22][23][24]. It has been noted that both operational and geometric perspectives are in general significant for resource theory [15]- [17], [28], [45]. Since Frobenius-norm has a geometric perspective [46], the basis independent measure of coherence [28] employed here clearly has geometric interpretation.…”

Section: Discussionmentioning

confidence: 99%

“…The invariance of the Frobenius norm under unitary transformation [28] leads to preservation of this basis independent measure of coherence for small uncertainty wave packets, since a pure basis rotation is unable to impact the value of coherence even for large boosts. So, if there are two parties Alice (O) and Bob (O Λ ) who do not share any reference frame, and suppose Alice possesses a single party state whose spread in momentum is narrow enough.…”

Section: Coherence Of a Spin-1/2 Particle With Gaussian Momentum mentioning

confidence: 99%

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

Chatterjee

Majumdar

2017

Phys. Rev. A

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We consider the effect of relativistic boosts on single particle Gaussian wave packets. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence it is shown that in general the coherence decays with the increase of the momentum of the state, as well as the boost applied to it. Employing a basis-independent formulation, we show however, that coherence may be preserved even for large boosts applied on narrow uncertainty wave packets. Our result is exemplified quantitatively for practically realizable neutron wave functions.

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“…Based on the irreducible representation of the symmetry group and the Frobenius norm 22 , the SSD ranging from zero to unity is more capable to identify various nature of symmetries such as symmetry breaking, accidental degeneracy and spontaneous symmetry breaking 23 , in contrast to the previous explorations based on the abstract concepts of fuzz set 24 and transform information 25 . Recently, it was applied to the Frobenius norm-based measures for quantum coherence and asymmetry 26 .…”

Section: Introductionmentioning

confidence: 99%

Vector Form of Symmetry Degree

Dong

Zhang

Sun

et al. 2017

Sci Rep

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AbsractSymmetry degree is utilized to characterize the asymmetry of a physical system with respect to a symmetry group. The scalar form of symmetry degree (SSD) based on Frobenius-norm has been introduced recently to present a quantitative description of symmetry. Here we present the vector form of the symmetry degree (VSD) which possesses more advantages than the SSD. Mathematically, the dimension of VSD is defined as the conjugacy class number of the symmetry group, the square length of the VSD gives rise to the SSD and the direction of VSD is determined by the orders of the conjugacy classes. The merits of applying VSD both for finite and infinite symmetry groups include the additional information of broken symmetry operators with single symmetry breaking perturbation, and the capability of distinguishing distinct symmetry breaking perturbations which exactly give rise to degenerate SSD. Additionally, the VSD for physical systems under symmetry breaking perturbations can be regarded as a projection of the initial VSD without any symmetry breaking perturbations, which can be described by an evolution equation. There are the same advantages by applying VSD for the accidental degeneracy and spontaneous symmetry breaking.

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Frobenius-norm-based measures of quantum coherence and asymmetry

Cited by 47 publications

References 84 publications

Maximal coherence in a generic basis

Maximal coherence in a generic basis

Preservation of quantum coherence under Lorentz boost for narrow uncertainty wave packets

Vector Form of Symmetry Degree

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