94 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
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
A Generic Security Proof for Quantum Key Distribution
Quantum key distribution allows two parties, traditionally known as Alice and
Bob, to establish a secure random cryptographic key if, firstly, they have
access to a quantum communication channel, and secondly, they can exchange
classical public messages which can be monitored but not altered by an
eavesdropper, Eve. Quantum key distribution provides perfect security because,
unlike its classical counterpart, it relies on the laws of physics rather than
on ensuring that successful eavesdropping would require excessive computational
effort. However, security proofs of quantum key distribution are not trivial
and are usually restricted in their applicability to specific protocols. In
contrast, we present a general and conceptually simple proof which can be
applied to a number of different protocols. It relies on the fact that a
cryptographic procedure called privacy amplification is equally secure when an
adversary's memory for data storage is quantum rather than classical.Comment: Analysis of B92 protocol adde
Quantum Algorithms Revisited
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. A common pattern underpinning quantum algorithms can be
identified when quantum computation is viewed as multi-particle interference.
We use this approach to review (and improve) some of the existing quantum
algorithms and to show how they are related to different instances of quantum
phase estimation. We provide an explicit algorithm for generating any
prescribed interference pattern with an arbitrary precision.Comment: 18 pages, LaTeX, 7 figures. Submitted to Proc. Roy. Soc. Lond.
Reply to the comment on "Quantum principle of relativity"
We discuss critical remarks raised by Horodecki towards our work on the
connection between superluminal extension of special relativity and fundamental
aspects of quantum theory
Quantum Computers and Dissipation
We analyse dissipation in quantum computation and its destructive impact on
efficiency of quantum algorithms. Using a general model of decoherence, we
study the time evolution of a quantum register of arbitrary length coupled with
an environment of arbitrary coherence length. We discuss relations between
decoherence and computational complexity and show that the quantum
factorization algorithm must be modified in order to be regarded as efficient
and realistic.Comment: 20 pages, Latex, 7 Postscript figure
Perfect state transfer in quantum spin networks
We propose a class of qubit networks that admit perfect transfer of any
quantum state in a fixed period of time. Unlike many other schemes for quantum
computation and communication, these networks do not require qubit couplings to
be switched on and off. When restricted to N-qubit spin networks of identical
qubit couplings, we show that 2 log_3 N is the maximal perfect communication
distance for hypercube geometries. Moreover, if one allows fixed but different
couplings between the qubits then perfect state transfer can be achieved over
arbitrarily long distances in a linear chain.Comment: 4 pages, 1 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
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