1,213 research outputs found
Quantum Algorithms: Entanglement Enhanced Information Processing
We discuss the fundamental role of entanglement as the essential nonclassical
feature providing the computational speed-up in the known quantum algorithms.
We review the construction of the Fourier transform on an Abelian group and the
principles underlying the fast Fourier transform algorithm. We describe the
implementation of the FFT algorithm for the group of integers modulo 2^n in the
quantum context, showing how the group-theoretic formalism leads to the
standard quantum network and identifying the property of entanglement that
gives rise to the exponential speedup (compared to the classical FFT). Finally
we outline the use of the Fourier transform in extracting periodicities, which
underlies its utility in the known quantum algorithms.Comment: 17 pages latex, no figures. To appear in Phil. Trans. Roy. Soc.
(Lond.) 1998, Proceedings of Royal Society Discussion Meeting ``Quantum
Computation: Theory and Experiment'', held in November 199
Optimal State Discrimination Using Particle Statistics
We present an application of particle statistics to the problem of optimal
ambiguous discrimination of quantum states. The states to be discriminated are
encoded in the internal degrees of freedom of identical particles, and we use
the bunching and antibunching of the external degrees of freedom to
discriminate between various internal states. We show that we can achieve the
optimal single-shot discrimination probability using only the effects of
particle statistics. We discuss interesting applications of our method to
detecting entanglement and purifying mixed states. Our scheme can easily be
implemented with the current technology
Staying adiabatic with unknown energy gap
We introduce an algorithm to perform an optimal adiabatic evolution that
operates without an apriori knowledge of the system spectrum. By probing the
system gap locally, the algorithm maximizes the evolution speed, thus
minimizing the total evolution time. We test the algorithm on the Landau-Zener
transition and then apply it on the quantum adiabatic computation of 3-SAT: The
result is compatible with an exponential speed-up for up to twenty qubits with
respect to classical algorithms. We finally study a possible algorithm
improvement by combining it with the quantum Zeno effect.Comment: 4 pages, 4 figure
Optimal purification of single qubits
We introduce a new decomposition of the multiqubit states of the form
and employ it to construct the optimal single qubit
purification procedure. The same decomposition allows us to study optimal
quantum cloning and state estimation of mixed states.Comment: 4 pages, 1 figur
Quantum key distribution over 30km of standard fiber using energy-time entangled photon pairs: a comparison of two chromatic dispersion reduction methods
We present a full implementation of a quantum key distribution system using
energy-time entangled photon pairs and functioning with a 30km standard telecom
fiber quantum channel. Two bases of two orthogonal states are implemented and
the setup is quite robust to environmental constraints such as temperature
variation. Two different ways to manage chromatic dispersion in the quantum
channel are discussed.Comment: 10 pages, 4 figure
Geometric phase for an adiabatically evolving open quantum system
We derive an elegant solution for a two-level system evolving adiabatically
under the influence of a driving field with a time-dependent phase, which
includes open system effects such as dephasing and spontaneous emission. This
solution, which is obtained by working in the representation corresponding to
the eigenstates of the time-dependent Hermitian Hamiltonian, enables the
dynamic and geometric phases of the evolving density matrix to be separated and
relatively easily calculated.Comment: 10 pages, 0 figure
Berry phase in a non-isolated system
We investigate the effect of the environment on a Berry phase measurement
involving a spin-half. We model the spin+environment using a biased spin-boson
Hamiltonian with a time-dependent magnetic field. We find that, contrary to
naive expectations, the Berry phase acquired by the spin can be observed, but
only on timescales which are neither too short nor very long. However this
Berry phase is not the same as for the isolated spin-half. It does not have a
simple geometric interpretation in terms of the adiabatic evolution of either
bare spin-states or the dressed spin-resonances that remain once we have traced
out the environment. This result is crucial for proposed Berry phase
measurements in superconducting nanocircuits as dissipation there is known to
be significant.Comment: 4 pages (revTeX4) 2 fig. This version has MAJOR changes to equation
NMR GHZ
We describe the creation of a Greenberger-Horne-Zeilinger (GHZ) state of the
form |000>+|111> (three maximally entangled quantum bits) using Nuclear
Magnetic Resonance (NMR). We have successfully carried out the experiment using
the proton and carbon spins of trichloroethylene, and confirmed the result
using state tomography. We have thus extended the space of entangled quantum
states explored systematically to three quantum bits, an essential step for
quantum computation.Comment: 4 pages in RevTex, 3 figures, the paper is also avalaible at
http://qso.lanl.gov/qc
Quantum Cryptography with Coherent States
The safety of a quantum key distribution system relies on the fact that any
eavesdropping attempt on the quantum channel creates errors in the
transmission. For a given error rate, the amount of information that may have
leaked to the eavesdropper depends on both the particular system and the
eavesdropping strategy. In this work, we discuss quantum cryptographic
protocols based on the transmission of weak coherent states and present a new
system, based on a symbiosis of two existing ones, and for which the
information available to the eavesdropper is significantly reduced. This system
is therefore safer than the two previous ones. We also suggest a possible
experimental implementation.Comment: 20 pp. Revtex, Figures available from the authors upon request, To be
published in PRA (March 95
Multipartite entanglement in quantum spin chains
We study the occurrence of multipartite entanglement in spin chains. We show
that certain genuine multipartite entangled states, namely W states, can be
obtained as ground states of simple XX type ferromagnetic spin chains in a
transverse magnetic field, for any number of sites. Moreover, multipartite
entanglement is proven to exist even at finite temperatures. A transition from
a product state to a multipartite entangled state occurs when decreasing the
magnetic field to a critical value. Adiabatic passage through this point can
thus lead to the generation of multipartite entanglement.Comment: 4 pages, 1 figur
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