Science - 06.12.2019

extendedVplrange]. This provides further
evidence that the edge electrons contributing
to the quantum oscillations in the floating
island configuration are indeed incorporated
into the metal. An additional, smaller sig-
nal of fixed period 15 mV is visible in both
configurations (in the form of direct oscilla-
tions or of an amplitude modulation), which
might originate from the progressive charging
of a nearby defect.
This experimental work demonstrates that
the Coulomb interaction has two facets. It can
both destroy and preserve quantum effects.
Although a metallic island is often pictured as
a floating reservoir of uncorrelated electrons
( 8 , 33 ), we establish that a high-fidelity elec-
tron quantum state transfer can take place
across it, enforced by the Coulomb charging
energy. This provides a means to overcome
limitations imposed by the decoherence of
individual electrons. Moreover, the observed
universal 2pelectron phase shift for one elem-
entary chargeeon the island can allow for a
strong entanglement of single-electron states,
both between themselves or with other quan-
tum degrees of freedom, with a negligible
loss of coherence. Such controllable, strong-
coupling mechanism constitutes a key ele-
ment in the context of quantum Hall edges
envisioned as platformsfor the manipulation
and transfer of quantum information via pro-
pagating electrons ( 21 , 34 – 39 ). In particular, it
is very well suited to implementing quantum
gates for these“flying qubits,”such as the
CNOT proposal involving a conditional phase
shift ofpdescribed in ( 38 ).

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ACKNOWLEDGMENTS

We thank P. Brouwer, L. Glazman, C. Mora, H. Sim, and E. Sukhorukov

for illuminating discussions.Funding:This work was supported

by the French RENATECH network, the national French program

‘Investissements d’Avenir’(Labex NanoSaclay, ANR-10-LABX-0035),

and the French National Research Agency (projects QuTherm,

ANR-16-CE30-0010, and SIM-CIRCUIT, ANR-18-CE47-0014-01).

Author contributions:E.S. and H.D. performed the experiment and

analyzed the data with help from A.Aa., A.An., and F.P.; F.P.

fabricated the sample with assistance from E.S and H.D.; A.C. and

U.G. grew the 2DEG; F.P. led the project and wrote the manuscript

with input from A.Aa., A.An., E.S., H.D., and U.GCompeting

interests:The authors declare no competing financial interests.

Data and materials availability:The data shown in the paper are

available at Zenodo ( 40 ). Correspondence and requests for materials

should be addressed to F.P. ([email protected]).

SUPPLEMENTARY MATERIALS

science.sciencemag.org/content/366/6470/1243/suppl/DC1

Materials and Methods

Figs. S1 to S5

24 January 2019; accepted 6 November 2019

10.1126/science.aaw7856

Duprezet al.,Science 366 , 1243–1247 (2019) 6 December 2019 4of4

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