87 research outputs found
Experimental quantum computing without entanglement
Entanglement is widely believed to lie at the heart of the advantages offered
by a quantum computer. This belief is supported by the discovery that a
noiseless (pure) state quantum computer must generate a large amount of
entanglement in order to offer any speed up over a classical computer. However,
deterministic quantum computation with one pure qubit (DQC1), which employs
noisy (mixed) states, is an efficient model that generates at most a marginal
amount of entanglement. Although this model cannot implement any arbitrary
algorithm it can efficiently solve a range of problems of significant
importance to the scientific community. Here we experimentally implement a
first-order case of a key DQC1 algorithm and explicitly characterise the
non-classical correlations generated. Our results show that while there is no
entanglement the algorithm does give rise to other non-classical correlations,
which we quantify using the quantum discord - a stronger measure of
non-classical correlations that includes entanglement as a subset. Our results
suggest that discord could replace entanglement as a necessary resource for a
quantum computational speed-up. Furthermore, DQC1 is far less resource
intensive than universal quantum computing and our implementation in a scalable
architecture highlights the model as a practical short-term goal.Comment: 5 pages, 4 figure
Quantum Computing Without Entanglement
It is generally believed that entanglement is essential for quantum
computing. We present here a few simple examples in which quantum computing
without entanglement is better than anything classically achievable, in terms
of the reliability of the outcome after a xed number of oracle calls. Using a
separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa
problem and the Simon problem can be solved more reliably by a quantum computer
than by the best possible classical algorithm, even probabilistic. We conclude
that: (a) entanglement is not essential for quantum computing; and (b) some
advantage of quantum algorithms over classical algorithms persists even when
the quantum state contains an arbitrarily small amount of information|that is,
even when the state is arbitrarily close to being totally mixed.Comment: 18 pages. Presented at FoCM'02 (Aug 2002, see
http://www.cs.technion.ac.il/~danken/pub/QCnoEnt.pdf), QIP'03 (Dec 2002, see
http://www.msri.org/publications/ln/msri/2002/qip/brassard/1/), Qubit'03 (Apr
2003, see http://www.cs.technion.ac.il/~talmo/Qubitconf/QUBIT-2003/program/
A new criteria for zero quantum discord
We propose a new criterion to judge zero quantum discord for arbitrary
bipartite states. A bipartite quantum state has zero quantum discord if and
only if all blocks of its density matrix are normal matrices and commute with
each other. Given a bipartite state with zero quantum discord, how to find out
the set of local projectors, which do not disturb the whole state after being
imposed on one subsystem, is also presented. A class of two-qubit X-state is
used to test the criterion, and an experimental scheme is proposed to realize
it. Consequently, we prove that the positive operator-valued measurement can
not extinguish the quantum correlation of a bipartite state with nonzero
quantum discord.Comment: 10 pages, 1 figur
Quantum Advantage without Entanglement
We study the advantage of pure-state quantum computation without entanglement
over classical computation. For the Deutsch-Jozsa algorithm we present the
maximal subproblem that can be solved without entanglement, and show that the
algorithm still has an advantage over the classical ones. We further show that
this subproblem is of greater significance, by proving that it contains all the
Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and
Grover's algorithms we provide simple proofs that no non-trivial subproblems
can be solved by these algorithms without entanglement.Comment: 10 page
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