Quantifying algebraic asymmetry of Hamiltonian systems

Qin, Huihui; Fei, Shao-Ming; Sun, C. P.

doi:10.1088/1751-8121/ab5b27

Cited by 2 publications

(2 citation statements)

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“…Moreover, the relations between asymmetry and quantum correlations have been revealed in [16][17][18] and the properties of asymmetry such as universal freezing and no-broadcasting theorem for asymmetry have been studied in [19][20][21]. Besides, the asymmetry of the Hamiltonian has also been studied and used to reveal symmetry breaking and quantum phase transition [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Quantifying asymmetry via generalized Wigner–Yanase–Dyson skew information

Sun

2021

J. Phys. A: Math. Theor.

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Asymmetry is a useful physical resource which quantifies the extent to which a quantum state breaks a symmetry. Based on the generalization of Wigner–Yanase–Dyson skew information of quantum states for any operator (not necessarily Hermitian), we introduce an asymmetry measure of a quantum state with respect to a compact Lie group as the average skew information of this state for each operator in its unitary representation and prove that it meets the requirements for the resource theory of asymmetry. For several significant symmetry groups, such as the group U(1), the full unitary group, the local unitary group, the group UU, the group , and the orthogonal group OO, we calculate the asymmetry of quantum states. Furthermore, we compare the asymmetry measure of quantum states with respect to a compact Lie group with the asymmetry measure of quantum states with respect to the corresponding Lie algebras introduced in (2020 Europhys. Lett. 130 30004 ) and illustrate that they are closely related, although they capture different aspects of asymmetry of quantum states.

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Section: Introductionmentioning

confidence: 99%

Quantifying asymmetry via generalized Wigner–Yanase–Dyson skew information

Sun

2021

J. Phys. A: Math. Theor.

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“…Actions on the larger system cannot, in general, be replicated by actions on the smaller system. The related but distinct notions of when nonlocal operations on a bipartite state can have support on just a single subsystem and when the state dynamics are themselves symmetric, have been recently investigated in [28] and [29], respectively.…”

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confidence: 99%

Operational symmetries of entangled states

Tzitrin¹,

Goldberg²,

Cresswell³

2020

J. Phys. A: Math. Theor.

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Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental property of entanglement does and does not hold, including multipartite and mixed states. Our results lead to a method for quantifying entanglement based on operational symmetries and has connections to quantum steering, envariance, the Reeh-Schlieder theorem, and classical entanglement.

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Quantifying algebraic asymmetry of Hamiltonian systems

Cited by 2 publications

References 50 publications

Quantifying asymmetry via generalized Wigner–Yanase–Dyson skew information

Quantifying asymmetry via generalized Wigner–Yanase–Dyson skew information

Operational symmetries of entangled states

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