Qudit hypergraph states

Steinhoff, F. E. S.; Ritz, Christina; Miklin, Nikolai; Gühne, Otfried

doi:10.1103/physreva.95.052340

Cited by 19 publications

(41 citation statements)

References 47 publications

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“…Moreover, this strategy can be turned into a homogeneous strategy with the same spectral gap [44], which is useful for fidelity estimation by Eq. (8). The standard deviation of this estimation satisfies…”

Section: B Maximally Entangled States and Ghz Statesmentioning

confidence: 88%

“…(159) is homogeneous, it can also be used for fidelity estimation by virtue of Eq. (8). The standard deviation of this estimation satisfies…”

Section: Stabilizer Statesmentioning

confidence: 88%

“…For example, bipartite entangled states, especially maximally entangled states, are crucial to quantum teleportation, dense coding, and quantum cryptography [2,3]. Multipartite entangled states, such as graph states [4] and hypergraph states [5][6][7][8][9] are especially useful in (blind) measurement-based quantum computation (MBQC) [10][11][12][13][14][15][16][17][18][19][20], quantum error correction [21,22], quantum networks [23][24][25], and foundation studies [26][27][28][29]. Another important class of multipartite states, including Dicke states [30,31], are useful in quantum metrology [32].…”

Section: Introductionmentioning

confidence: 99%

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General framework for verifying pure quantum states in the adversarial scenario

Zhu

Hayashi

2019

Phys. Rev. A

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Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is know about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario. This paper is an extended version of the companion paper [1].

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Section: B Maximally Entangled States and Ghz Statesmentioning

confidence: 88%

“…(159) is homogeneous, it can also be used for fidelity estimation by virtue of Eq. (8). The standard deviation of this estimation satisfies…”

Section: Stabilizer Statesmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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General framework for verifying pure quantum states in the adversarial scenario

Zhu

Hayashi

2019

Phys. Rev. A

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“…The Hamiltonian of a BNS system, including the leading-order tidal excitations of the stars, can be expressed as [37,38]…”

Section: Basic Formalismmentioning

confidence: 99%

“…With sufficiently accurate orbit model, it might be possible to combine f-mode emission from different pericenter encounter cycles to boost the signal-to-noise ratio of detection, e.g., with the coherent stacking method [34][35][36]. While the formation of such systems may require rather restrictive initial parameters, it is still important to characterize the tidal effect in medium-low eccentricity BNSs, in addition to the understanding of equilibrium and dynamic tide in the circular orbit limit [37,38].…”

Section: Introductionmentioning

confidence: 99%

Inspiralling eccentric binary neutron stars: Orbital motion and tidal resonance

Yang

2019

Phys. Rev. D

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We study the orbital evolution of eccentric binary neutron stars. The motion follows a Quasi-Keplarian orbit with perturbations due to tidal couplings. We find that the tidal interaction between stars contributes to orbital precession in addition to the Post-Newtonian procession. The coupling between the angular and radial motion of the binary also excites a series of harmonics in the stars' oscillation. In the small eccentricity limit, this coupling mainly gives rise to an additional orbital resonance, with the orbital frequency being one third of the f-mode frequency. For a binary with initial eccentricity ∼ 0.2 at 50Hz orbital frequency, the presence of this tidal resonance introduces ∼ O(0.5) phase shift in the gravitational waveform till merger, subject to uncertainties in neutron star equation of state and the distribution of binary component masses. Such phase shift in the late-inspiral stage is likely detectable with third-generation gravitational-wave detectors.

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Entanglement entropy and the colored Jones polynomial

Balasubramanian

DeCross

Fliss

et al. 2018

J. High Energ. Phys.

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We study the multi-party entanglement structure of states in Chern-Simons theory created by performing the path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU (2), the wavefunctions of these states (in a particular basis) are the colored Jones polynomials of the corresponding links. We first review the case of U (1) Chern-Simons theory where these are stabilizer states, a fact we use to re-derive an explicit formula for the entanglement entropy across a general link bipartition. We then present the following results for SU (2) Chern-Simons theory: (i) The entanglement entropy for a bipartition of a link gives a lower bound on the genus of surfaces in the ambient S 3 separating the two sublinks. (ii) All torus links (namely, links which can be drawn on the surface of a torus) have a GHZ-like entanglement structure -i.e., partial traces leave a separable state. By contrast, through explicit computation, we test in many examples that hyperbolic links (namely, links whose complements admit hyperbolic structures) have Wlike entanglement -i.e., partial traces leave a non-separable state. (iii) Finally, we consider hyperbolic links in the complexified SL(2, C) Chern-Simons theory, which is closely related to 3d Einstein gravity with a negative cosmological constant. In the limit of small Newton constant, we discuss how the entanglement structure is controlled by the Neumann-Zagier potential on the moduli space of hyperbolic structures on the link complement.

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Qudit hypergraph states

Cited by 19 publications

References 47 publications

General framework for verifying pure quantum states in the adversarial scenario

General framework for verifying pure quantum states in the adversarial scenario

Inspiralling eccentric binary neutron stars: Orbital motion and tidal resonance

Entanglement entropy and the colored Jones polynomial

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