21,956 research outputs found
Optimal quantum control of Bose Einstein condensates in magnetic microtraps
Transport of Bose-Einstein condensates in magnetic microtraps, controllable
by external parameters such as wire currents or radio-frequency fields, is
studied within the framework of optimal control theory (OCT). We derive from
the Gross-Pitaevskii equation the optimality system for the OCT fields that
allow to efficiently channel the condensate between given initial and desired
states. For a variety of magnetic confinement potentials we study transport and
wavefunction splitting of the condensate, and demonstrate that OCT allows to
drastically outperfrom more simple schemes for the time variation of the
microtrap control parameters.Comment: 11 pages, 7 figure
Option Pricing in Multivariate Stochastic Volatility Models of OU Type
We present a multivariate stochastic volatility model with leverage, which is
flexible enough to recapture the individual dynamics as well as the
interdependencies between several assets while still being highly analytically
tractable.
First we derive the characteristic function and give conditions that ensure
its analyticity and absolute integrability in some open complex strip around
zero. Therefore we can use Fourier methods to compute the prices of multi-asset
options efficiently. To show the applicability of our results, we propose a
concrete specification, the OU-Wishart model, where the dynamics of each
individual asset coincide with the popular Gamma-OU BNS model. This model can
be well calibrated to market prices, which we illustrate with an example using
options on the exchange rates of some major currencies. Finally, we show that
covariance swaps can also be priced in closed form.Comment: 28 pages, 5 figures, to appear in SIAM Journal on Financial
Mathematic
Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
A few simply-stated rules govern the entanglement patterns that can occur in
mutually unbiased basis sets (MUBs), and constrain the combinations of such
patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1
MUBs. We consider Hilbert spaces of prime power dimension (as realized by
systems of N prime-state particles, or qupits), where full complements are
known to exist, and we assume only that MUBs are eigenbases of generalized
Pauli operators, without using a particular construction. The general rules
include the following: 1) In any MUB, a particular qupit appears either in a
pure state, or totally entangled, and 2) in any full MUB complement, each qupit
is pure in p+1 bases (not necessarily the same ones), and totally entangled in
the remaining p^N-p. It follows that the maximum number of product bases is
p+1, and when this number is realized, all remaining p^N-p bases in the
complement are characterized by the total entanglement of every qupit. This
"standard distribution" is inescapable for two qupits (of any p), where only
product and generalized Bell bases are admissible MUB types. This and the
following results generalize previous results for qubits and qutrits. With
three qupits there are three MUB types, and a number of combinations (p+2) are
possible in full complements. With N=4, there are 6 MUB types for p=2, but new
MUB types become possible with larger p, and these are essential to the
realization of full complements. With this example, we argue that new MUB
types, showing new entanglement characteristics, should enter with every step
in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs
should play critical roles in filling complements.Comment: 27 pages, one figure, to be submitted to Physical Revie
Unified derivations of measurement-based schemes for quantum computation
We present unified, systematic derivations of schemes in the two known
measurement-based models of quantum computation. The first model (introduced by
Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed
entangled state, adaptive measurements on single qubits, and feedforward of the
measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308,
96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)])
uses adaptive two-qubit measurements that can be applied to arbitrary pairs of
qubits, and feedforward of the measurement results. The underlying principle of
our derivations is a variant of teleportation introduced by Zhou, Leung, and
Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two
measurement-based models of quantum computation and provide significantly
simpler schemes.Comment: 14 page
Ground-state geometric quantum computing in superconducting systems
We present a theoretical proposal for the implementation of geometric quantum
computing based on a Hamiltonian which has a doubly degenerate ground state.
Thus the system which is steered adiabatically, remains in the ground-state.
The proposed physical implementation relies on a superconducting circuit
composed of three SQUIDs and two superconducting islands with the charge states
encoding the logical states. We obtain a universal set of single-qubit gates
and implement a non-trivial two-qubit gate exploiting the mutual inductance
between two neighboring circuits, allowing us to realize a fully geometric
ground-state quantum computing. The introduced paradigm for the implementation
of geometric quantum computing is expected to be robust against environmental
effects.Comment: 9 pages, 5 figures. Final version with notation and typos correcte
Computation by measurements: a unifying picture
The ability to perform a universal set of quantum operations based solely on
static resources and measurements presents us with a strikingly novel viewpoint
for thinking about quantum computation and its powers. We consider the two
major models for doing quantum computation by measurements that have hitherto
appeared in the literature and show that they are conceptually closely related
by demonstrating a systematic local mapping between them. This way we
effectively unify the two models, showing that they make use of interchangeable
primitives. With the tools developed for this mapping, we then construct more
resource-effective methods for performing computation within both models and
propose schemes for the construction of arbitrary graph states employing
two-qubit measurements alone.Comment: 13 pages, 18 figures, REVTeX
Estimating entanglement of unknown states
The experimental determination of entanglement is a major goal in the quantum
information field. In general the knowledge of the state is required in order
to quantify its entanglement. Here we express a lower bound to the robustness
of entanglement of a state based only on the measurement of the energy
observable and on the calculation of a separability energy. This allows the
estimation of entanglement dismissing the knowledge of the state in question.Comment: 3 pages, 1 figure. Comments welcome. V2: references updated. Accepted
version by Applied Physics Letter
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