5,593 research outputs found
Well-Rounded ideal lattices of cyclic cubic and quartic fields
In this paper, we find criteria for when cyclic cubic and cyclic quartic
fields have well-rounded ideal lattices. We show that every cyclic cubic field
has at least one well-rounded ideal. We also prove that there exist families of
cyclic quartic fields which have well-rounded ideals and explicitly construct
their minimal bases. In addition, for a given prime number , if a cyclic
quartic field has a unique prime ideal above , then we provide the necessary
and sufficient conditions for that ideal to be well-rounded. Moreover, in
cyclic quartic fields, we provide the prime decomposition of all odd prime
numbers and construct an explicit integral basis for every prime ideal.Comment: 26 page
Well-Rounded Twists of Ideal Lattices from Imaginary Quadratic Fields
In this paper, we investigate the properties of well-rounded twists of a
given ideal lattice of an imaginary quadratic field . We show that every
ideal lattice of has at least one well-rounded twist lattice. Moreover,
we provide an explicit algorithm to compute all well-rounded twists of .Comment: 24 page
High-efficiency WSi superconducting nanowire single-photon detectors for quantum state engineering in the near infrared
We report on high-efficiency superconducting nanowire single-photon detectors
based on amorphous WSi and optimized at 1064 nm. At an operating temperature of
1.8 K, we demonstrated a 93% system detection efficiency at this wavelength
with a dark noise of a few counts per second. Combined with cavity-enhanced
spontaneous parametric down-conversion, this fiber-coupled detector enabled us
to generate narrowband single photons with a heralding efficiency greater than
90% and a high spectral brightness of
photons/(smWMHz). Beyond single-photon generation at large rate,
such high-efficiency detectors open the path to efficient multiple-photon
heralding and complex quantum state engineering
Demonstration of Einstein-Podolsky-Rosen Steering Using Hybrid Continuous- and Discrete-Variable Entanglement of Light
Einstein-Podolsky-Rosen steering is known to be a key resource for one-sided
device-independent quantum information protocols. Here we demonstrate steering
using hybrid entanglement between continuous- and discrete-variable optical
qubits. To this end, we report on suitable steering inequalities and detail the
implementation and requirements for this demonstration. Steering is
experimentally certified by observing a violation by more than 5 standard
deviations. Our results illustrate the potential of optical hybrid entanglement
for applications in heterogeneous quantum networks that would interconnect
disparate physical platforms and encodings
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