339 research outputs found
No-go theorems for \psi-epistemic models based on a continuity assumption
The quantum state \psi is a mathematical object used to determine the
probabilities of different outcomes when measuring a physical system. Its
fundamental nature has been the subject of discussions since the inception of
quantum theory: is it ontic, that is, does it correspond to a real property of
the physical system? Or is it epistemic, that is, does it merely represent our
knowledge about the system? Assuming a natural continuity assumption and a weak
separability assumption, we show here that epistemic interpretations of the
quantum state are in contradiction with quantum theory. Our argument is
different from the recent proof of Pusey, Barrett, and Rudolph and it already
yields a non-trivial constraint on \psi-epistemic models using a single copy of
the system in question.Comment: Version 1 contains both theory and an illustrative experiment.
Version 2 contains only the theory (the experiment with expanded discussion
will be posted separatly at a later date). The main novelty of Version 2 is a
detailed comparison in appendix 2 with L. Hardy arXiv:1205.14396. Version 2
is 6 pages of text and 1 figure; v3: minor change
Non locality, closing the detection loophole and communication complexity
It is shown that the detection loophole which arises when trying to rule out
local realistic theories as alternatives for quantum mechanics can be closed if
the detection efficiency is larger than
where is the dimension of the entangled system. Furthermore it is argued
that this exponential decrease of the detector efficiency required to close the
detection loophole is almost optimal. This argument is based on a close
connection that exists between closing the detection loophole and the amount of
classical communication required to simulate quantum correlation when the
detectors are perfect.Comment: 4 pages Latex, minor typos correcte
Lower bound on the number of Toffoli gates in a classical reversible circuit through quantum information concepts
The question of finding a lower bound on the number of Toffoli gates in a
classical reversible circuit is addressed. A method based on quantum
information concepts is proposed. The method involves solely concepts from
quantum information - there is no need for an actual physical quantum computer.
The method is illustrated on the example of classical Shannon data compression.Comment: 4 pages, 2 figures; revised versio
Error Filtration and Entanglement Purification for Quantum Communication
The key realisation which lead to the emergence of the new field of quantum
information processing is that quantum mechanics, the theory that describes
microscopic particles, allows the processing of information in fundamentally
new ways. But just as in classical information processing, errors occur in
quantum information processing, and these have to be corrected. A fundamental
breakthrough was the realisation that quantum error correction is in fact
possible. However most work so far has not been concerned with technological
feasibility, but rather with proving that quantum error correction is possible
in principle. Here we describe a method for filtering out errors and
entanglement purification which is particularly suitable for quantum
communication. Our method is conceptually new, and, crucially, it is easy to
implement in a wide variety of physical systems with present day technology and
should therefore be of wide applicability.Comment: 23 pages (latex) and 4 postscript figure
Device independent state estimation based on Bell's inequalities
The only information available about an alleged source of entangled quantum
states is the amount by which the Clauser-Horne-Shimony-Holt (CHSH)
inequality is violated: nothing is known about the nature of the system or the
measurements that are performed. We discuss how the quality of the source can
be assessed in this black-box scenario, as compared to an ideal source that
would produce maximally entangled states (more precisely, any state for which
). To this end, we introduce several inequivalent notions of
fidelity, each one related to the use one can make of the source after having
assessed it; and we derive quantitative bounds for each of them in terms of the
violation . We also derive a lower bound on the entanglement of the source
as a function of only.Comment: 8 pages, 2 figures. Added appendices containing proof
Greenberger-Horne-Zeilinger paradoxes for many qudits
We construct GHZ contradictions for three or more parties sharing an
entangled state, the dimension d of each subsystem being an even integer
greater than 2. The simplest example that goes beyond the standard GHZ paradox
(three qubits) involves five ququats (d=4). We then examine the criteria a GHZ
paradox must satisfy in order to be genuinely M-partite and d-dimensional.Comment: 5 pages RevTe
Security of Quantum Bit-String Generation
We consider the cryptographic task of bit-string generation. This is a
generalisation of coin tossing in which two mistrustful parties wish to
generate a string of random bits such that an honest party can be sure that the
other cannot have biased the string too much. We consider a quantum protocol
for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004),
that is feasible with present day technology. We introduce security conditions
based on the average bias of the bits and the Shannon entropy of the string.
For each, we prove rigorous security bounds for this protocol in both noiseless
and noisy conditions under the most general attacks allowed by quantum
mechanics. Roughly speaking, in the absence of noise, a cheater can only bias
significantly a vanishing fraction of the bits, whereas in the presence of
noise, a cheater can bias a constant fraction, with this fraction depending
quantitatively on the level of noise. We also discuss classical protocols for
the same task, deriving upper bounds on how well a classical protocol can
perform. This enables the determination of how much noise the quantum protocol
can tolerate while still outperforming classical protocols. We raise several
conjectures concerning both quantum and classical possibilities for large n
cryptography. An experiment corresponding to the scheme analysed in this paper
has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A
corresponding experiment is reported in quant-ph/040812
Experimental quantum key distribution over highly noisy channels
Error filtration is a method for encoding the quantum state of a single
particle into a higher dimensional Hilbert space in such a way that it becomes
less sensitive to phase noise. We experimentally demonstrate this method by
distributing a secret key over an optical fiber whose noise level otherwise
precludes secure quantum key distribution. By filtering out the phase noise, a
bit error rate of 15.3% +/- 0.1%, which is beyond the security limit, can be
reduced to 10.6% +/- 0.1%, thereby guaranteeing the cryptographic security.Comment: 4 pages, 2 figure
Communication of Spin Directions with Product States and Finite Measurements
Total spin eigenstates can be used to intrinsically encode a direction, which
can later be decoded by means of a quantum measurement. We study the optimal
strategy that can be adopted if, as is likely in practical applications, only
product states of -spins are available. We obtain the asymptotic behaviour
of the average fidelity which provides a proof that the optimal states must be
entangled. We also give a prescription for constructing finite measurements for
general encoding eigenstates.Comment: 4 pages, minor changes, version to appear in PR
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