Scaling Laws for the Decay of Multiqubit Entanglement

I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tri-partite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tri-partite GHZ and W-type entanglement and compare the evolution of their detection capabilites with the evolution of the negativity, bi-partite concurrence, and tri-partite negativity. Interestingly, I find a state in which there is no concurrence or tri-partite negativity but there is entanglement. Finally, I utilize a three qubit quantum error correction (QEC) code to address how ESD affects the abilities of quantum error correction.

Section: Introductionmentioning

confidence: 99%

“…Entanglement may be present in a system but still not be practically useful [7]. For entanglement to be useful its presence should be efficiently detectable experimentally.…”

Section: Introductionmentioning

confidence: 99%

Tripartite entanglement witnesses and entanglement sudden death

Weinstein

2009

“…From a more fundamental perspective, the understanding of the entanglement properties and their manipulation at the macroscopic level is also of importance to understand the quantum to classical transition [5,6]. It is worth noticing that due to the exponential growth of the Hilbert space dimension with the number of parties N , an exact numerical simulation of such systems with classical computer is not possible when N becomes of the order of some tens.…”

Section: Introductionmentioning

confidence: 99%

Generalized spin-squeezing inequalities for particle number with quantum fluctuations

Saideh¹,

Felicetti²,

Coudreau³

et al. 2016

Particle number fluctuations, no matter how small, are present in experimental set-ups. One should rigorously take these fluctuations into account, especially, for entanglement detection. In this context, we generalize the spin squeezing inequalities introduced by Tóth et al. in Ref.[1]. These new inequalities are fulfilled by all separable states even when the number of particle is not constant, and may present quantum fluctuations. These inequalities are useful for detecting entanglement in many-body systems when the super-selection rule does not apply, or when only a subspace of the total systems Hilbert space is considered. We also define general dichotomic observables for which we obtain a coordinate independent form of the generalized spin squeezing inequalities. We give an example where our generalized coordinate independent spin squeezing inequalities present a clear advantage over the original ones.

“…In addition to the difficulty in producing large entangled states, they are typically very sensitive to noise [5][6][7]. An alternative route to enhance the size of a system is through hyperentanglement [8], that is, the entanglement in multiple degrees of freedom (DOF) of a composite quantum system.…”

mentioning

confidence: 99%

Quantum-enhanced sensing from hyperentanglement

Walborn

Filho

2018

Self Cite

Hyperentanglement -simultaneous entanglement between multiple degrees of freedom of two or more systems -has been used to enhance quantum information tasks such as quantum communication and photonic quantum computing. Here we show that hyperentanglement can lead to increased quantum advantage in metrology, with contributions from the entanglement in each degree of freedom, allowing for Heisenberg scaling in the precision of parameter estimation. Our experiment employs photon pairs entangled in polarization and spatial degrees of freedom to estimate a small tilt angle of a mirror. Precision limits beyond shot noise are saturated through a simple binary measurement of the polarization state. The broad validity of the dynamics considered here implies that similar strategies based on hyperentanglement can offer improvement in a wide variety of metrological tasks.To exploit the advantage of quantum entanglement for tasks such as computation and metrology requires producing highdimensional quantum states composed of many entangled sub-systems [1][2][3][4]. In addition to the difficulty in producing large entangled states, they are typically very sensitive to noise [5][6][7]. An alternative route to enhance the size of a system is through hyperentanglement [8], that is, the entanglement in multiple degrees of freedom (DOF) of a composite quantum system. So far, hyperentanglement has found use in high-capacity quantum communication [9][10][11][12][13], photonic quantum computing [14,15], tests of quantum non-locality [16,17], and the direct characterization of entanglement [18] and quantum dynamics [19]. Here we demonstrate the usefulness of hyperentanglement in metrology, allowing one to reach the ultimate quantum precision limits, for the paradigmatic case of an interaction between two degrees of freedom of the same system. Examples of this type of evolution include the interaction between spin and momentum in a SternGerlach experiment, between internal and external DOF of trapped ions [20], or the polarization and spatial DOF of an optical field propagating through a birefringent medium [21].Our experiment employs hyperentangled photon pairs to monitor a tiny rotation of a mirror. Entanglement in both spatial and polarization DOF leads to increased quantum advantage in metrological sensing, allowing for Heisenberg scaling in the number of photons N used to probe the rotation: the precision of estimation becomes proportional to 1/N , instead of the shot-noise behavior ∝ 1/ √ N . Estimation of tilt angles of mirrors is important in several fields of science [22][23][24][25]. A common procedure consists in detecting the spatial or phase displacement of a laser beam reflected by the mirror [26][27][28][29][30][31][32]. Our method, on the other hand, is based solely on a binary polarization measurement at the output of an interferometer with a displaced input beam. This scheme takes advantage of both hyper-entanglement and beam displacement to increase the precision beyond the shot-noise limit.Precision measurements and F...