3,054 research outputs found
From quantum-codemaking to quantum code-breaking
This is a semi-popular overview of quantum entanglement as an important
physical resource in the field of data security and quantum computing. After a
brief outline of entanglement's key role in philosophical debates about the
meaning of quantum mechanics I describe its current impact on both cryptography
and cryptanalysis. The paper is based on the lecture given at the conference
"Geometric Issues in the Foundations of Science" (Oxford, June 1996) in honor
of Roger Penrose.Comment: 21 pages, LaTeX2e, psfig, multi3.cls, 1 eps figur
Symmetrizing Evolutions
We introduce quantum procedures for making -invariant the dynamics of
an arbitrary quantum system S, where is a finite group acting on the
space state of S. Several applications of this idea are discussed. In
particular when S is a N-qubit quantum computer interacting with its
environment and the symmetric group of qubit permutations, the
resulting effective dynamics admits noiseless subspaces. Moreover it is shown
that the recently introduced iterated-pulses schemes for reducing decoherence
in quantum computers fit in this general framework. The noise-inducing
component of the Hamiltonian is filtered out by the symmetrization procedure
just due to its transformation properties.Comment: Presentation improved, to appear in Phys. Lett. A. 5 pages LaTeX, no
figure
Against Quantum Noise
This is a brief description of how to protect quantum states from dissipation
and decoherence that arise due to uncontrolled interactions with the
environment. We discuss recoherence and stabilisation of quantum states based
on two techniques known as "symmetrisation" and "quantum error correction". We
illustrate our considerations with the most popular quantum-optical model of
the system-environment interaction, commonly used to describe spontaneous
emission, and show the benefits of quantum error correction in this case.Comment: 12 pages. Presented at the International Conference "Quantum Optics
IV", Jaszowiec, Poland, June 17-24 1997. An introductory overview of quantum
dissipation and error correction. Late submission to the archive due to
requests and the limited availability of the journa
Higher dimensional quantum communication in a curved spacetime: an efficient simulation of the propagation of the wavefront of a photon
A photon with a modulated wavefront can produce a quantum communication
channel in a larger Hilbert space. For example, higher dimensional quantum key
distribution (HD-QKD) can encode information in the transverse linear momentum
(LM) or orbital angular momentum (OAM) modes of a photon. This is markedly
different than using the intrinsic polarization of a photon. HD-QKD has
advantages for free space QKD since it can increase the communication
channel\~Os tolerance to bit error rate (BER) while maintaining or increasing
the channels bandwidth. We describe an efficient numerical simulation of the
propagation photon with an arbitrary complex wavefront in a material with an
isotropic but inhomogeneous index of refraction. We simulate the waveform
propagation of an optical vortex in a volume holographic element in the
paraxial approximation using an operator splitting method. We use this code to
analyze an OAM volume-holographic sorter. Furthermore, there are analogue
models of the evolution of a wavefront in the curved spacetime environs of the
Earth that can be constructed using an optical medium with a given index of
refraction. This can lead to a work-bench realization of a satellite HD-QKD
system.Comment: 20 pages, 7 figure
Quantum cryptography with polarizing interferometers
Cryptographic scheme proposed by Bennett, Brassard, and Mermin [Phys. Rev.
Lett. {\bf 68}, 557 (1992)] is reformulated in a version involving two
polarizing Mach-Zehnder interferometers. Such a form, although physically
equivalent to the original one, makes its security explicit, suggestive and
easy to explain to non-experts.Comment: revtex, 4 pages, 1 ps figur
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
Unambiguous Discrimination Between Linearly-Independent Quantum States
The theory of generalised measurements is used to examine the problem of
discriminating unambiguously between non-orthogonal pure quantum states.
Measurements of this type never give erroneous results, although, in general,
there will be a non-zero probability of a result being inconclusive. It is
shown that only linearly-independent states can be unambiguously discriminated.
In addition to examining the general properties of such measurements, we
discuss their application to entanglement concentration
How to Counteract Systematic Errors in Quantum State Transfer
In the absence of errors, the dynamics of a spin chain, with a suitably
engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum
state over large distances. Here, we propose encoding and decoding procedures
to recover perfectly from low rates of systematic errors. The encoding and
decoding regions, located at opposite ends of the chain, are small compared to
the length of the chain, growing linearly with the size of the error. We also
describe how these errors can be identified, again by only acting on the
encoding and decoding regions.Comment: 16 pages, 1 figur
Machines, Logic and Quantum Physics
Though the truths of logic and pure mathematics are objective and independent
of any contingent facts or laws of nature, our knowledge of these truths
depends entirely on our knowledge of the laws of physics. Recent progress in
the quantum theory of computation has provided practical instances of this, and
forces us to abandon the classical view that computation, and hence
mathematical proof, are purely logical notions independent of that of
computation as a physical process. Henceforward, a proof must be regarded not
as an abstract object or process but as a physical process, a species of
computation, whose scope and reliability depend on our knowledge of the physics
of the computer concerned.Comment: 19 pages, 8 figure
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