641 research outputs found
Three-way noiseless signal splitting in a parametric amplifier with quantum correlation
We demonstrate that a phase-insensitive parametric amplifier, coupled to a
quantum correlated source, can be used as a quantum information tap for
noiseless three-way signal splitting. We find that the output signals are
amplified noiselessly in two of the three output ports while the other can more
or less keep its original input size without adding noise. This scheme is able
to cascade and scales up for efficient information distribution in an optical
network. Furthermore, we find this scheme satisfies the criteria for a
non-ideal quantum non-demolition (QND) measurement and thus can serve as a QND
measurement device. With two readouts correlated to the input, we find this
scheme also satisfies the criterion for sequential QND measurement
Socle degrees for local cohomology modules of thickenings of maximal minors and sub-maximal Pfaffians
Let be the polynomial ring on the space of non-square generic matrices or
the space of odd-sized skew-symmetric matrices, and let be the
determinantal ideal of maximal minors or the ideal of
sub-maximal Pfaffians, respectively. Using desingularizations and
representation theory of the general linear group we expand upon work of
Raicu--Weyman--Witt to determine the -module structures of
and
, from which we get the
degrees of generators of these modules. As a consequence,
via graded local duality we answer a question of Wenliang Zhang on the socle
degrees of local cohomology modules of the form .Comment: Final version. Comments welcome
Joint measurement of multiple noncommuting parameters
Although quantum metrology allows us to make precision measurements beyond the standard quantum limit, it mostly works on the measurement of only one observable due to the Heisenberg uncertainty relation on the measurement precision of noncommuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other using the quantum entanglement between two systems. We focus on analyzing the performance of a SU(1,1) nonlinear interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple noncommuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement
Global Weinstein Type Theorem on Multiple Rotating Periodic Solutions for Hamiltonian Systems
This paper concerns the existence of multiple rotating periodic solutions for
dimensional convex Hamiltonian systems. For the symplectic orthogonal
matrix , the rotating periodic solution has the form of ,
which might be periodic, anti-periodic, subharmonic or quasi-periodic according
to the structure of . It is proved that there exist at least
geometrically distinct rotating periodic solutions on a given convex energy
surface under a pinched condition, so our result corresponds to the well known
Ekeland and Lasry's theorem on periodic solutions. It seems that this is the
first attempt to solve the symmetric quasi-periodic problem on the global
energy surface. In order to prove the result, we introduce a new index on
rotating periodic orbits.Comment: arXiv admin note: text overlap with arXiv:1812.0583
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