15,004 research outputs found
Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces
We propose an interferometric method for statistically discriminating between
nonorthogonal states in high dimensional Hilbert spaces for use in quantum
information processing. The method is illustrated for the case of photon
orbital angular momentum (OAM) states. These states belong to pairs of bases
that are mutually unbiased on a sequence of two-dimensional subspaces of the
full Hilbert space, but the vectors within the same basis are not necessarily
orthogonal to each other. Over multiple trials, this method allows
distinguishing OAM eigenstates from superpositions of multiple such
eigenstates. Variations of the same method are then shown to be capable of
preparing and detecting arbitrary linear combinations of states in Hilbert
space. One further variation allows the construction of chains of states
obeying recurrence relations on the Hilbert space itself, opening a new range
of possibilities for more abstract information-coding algorithms to be carried
out experimentally in a simple manner. Among other applications, we show that
this approach provides a simplified means of switching between pairs of
high-dimensional mutually unbiased OAM bases
A note on bounds for the cop number using tree decompositions
In this short note, we supply a new upper bound on the cop number in terms of
tree decompositions. Our results in some cases extend a previously derived
bound on the cop number using treewidth
Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
It is shown that quantum walks on one-dimensional arrays of special
linear-optical units allow the simulation of discrete-time Hamiltonian systems
with distinct topological phases. In particular, a slightly modified version of
the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states
of nonzero winding number and has topologically protected boundary states. In
the large-system limit this approach uses quadratically fewer resources to
carry out quantum simulations than previous linear-optical approaches and can
be readily generalized to higher-dimensional systems. The basic optical units
that implement this simulation consist of combinations of optical multiports
that allow photons to reverse direction
Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports
Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.This research was supported by the National Science Foundation EFRI-ACQUIRE Grant No. ECCS-1640968, NSF Grant No. ECCS-1309209, and by the Northrop Grumman NG Next. (ECCS-1640968 - National Science Foundation EFRI-ACQUIRE Grant; ECCS-1309209 - NSF Grant; Northrop Grumman NG Next
The association of ideas in English composition
Thesis (M.A.)--Boston University, 1948. This item was digitized by the Internet Archive
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