1,395 research outputs found
A contextual extension of Spekkens' toy model
Quantum systems show contextuality. More precisely, it is impossible to
reproduce the quantum-mechanical predictions using a non-contextual realist
model, i.e., a model where the outcome of one measurement is independent of the
choice of compatible measurements performed in the measurement context. There
has been several attempts to quantify the amount of contextuality for specific
quantum systems, for example, in the number of rays needed in a KS proof, or
the number of terms in certain inequalities, or in the violation, noise
sensitivity, and other measures. This paper is about another approach: to use a
simple contextual model that reproduces the quantum-mechanical contextual
behaviour, but not necessarily all quantum predictions. The amount of
contextuality can then be quantified in terms of additional resources needed as
compared with a similar model without contextuality. In this case the
contextual model needs to keep track of the context used, so the appropriate
measure would be memory. Another way to view this is as a memory requirement to
be able to reproduce quantum contextuality in a realist model. The model we
will use can be viewed as an extension of Spekkens' toy model [Phys. Rev. A 75,
032110 (2007)], and the relation is studied in some detail. To reproduce the
quantum predictions for the Peres-Mermin square, the memory requirement is more
than one bit in addition to the memory used for the individual outcomes in the
corresponding noncontextual model.Comment: 10 page
Loopholes in Bell Inequality Tests of Local Realism
Bell inequalities are intended to show that local realist theories cannot
describe the world. A local realist theory is one where physical properties are
defined prior to and independent of measurement, and no physical influence can
propagate faster than the speed of light. Quantum-mechanical predictions for
certain experiments violate the Bell inequality while a local realist theory
cannot, and this shows that a local realist theory cannot give those
quantum-mechanical predictions. However, because of unexpected circumstances or
"loopholes" in available experiment tests, local realist theories can reproduce
the data from these experiments. This paper reviews such loopholes, what effect
they have on Bell inequality tests, and how to avoid them in experiment.
Avoiding all these simultaneously in one experiment, usually called a
"loophole-free" or "definitive" Bell test, remains an open task, but is very
important for technological tasks such as device-independent security of
quantum cryptography, and ultimately for our understanding of the world.Comment: 42 pages, 2 figure
No information flow using statistical fluctuations, and quantum cryptography
The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306
(2003)] is examined in some detail, and found to work equally well using a
separable state. The protocol is in fact completely classical, based on simple
post-selection of suitable experimental runs. The quantum cryptography protocol
proposed in the same publication is also examined, and is found to indeed need
quantum properties for the system to be secure. However, the security test
proposed in the mentioned paper is found to be insufficient, and a modification
is proposed here that will ensure security.Comment: revtex4, 9 page
Comment on "New Results on Frame-Proof Codes and Traceability Schemes"
In the paper "New Results on Frame-Proof Codes and Traceability Schemes" by
Reihaneh Safavi-Naini and Yejing Wang [IEEE Trans. Inform. Theory, vol. 47, no.
7, pp. 3029-3033, Nov. 2001], there are lower bounds for the maximal number of
codewords in binary frame-proof codes and decoders in traceability schemes.
There are also existence proofs using a construction of binary frame-proof
codes and traceability schemes. Here it is found that the main results in the
referenced paper do not hold.Comment: 3 page
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Query complexity is a common tool for comparing quantum and classical
computation, and it has produced many examples of how quantum algorithms differ
from classical ones. Here we investigate in detail the role that oracles play
for the advantage of quantum algorithms. We do so by using a simulation
framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms
that solve some problems with the same success probability and number of
queries as the quantum algorithms. The framework can be simulated using only
classical resources at a constant overhead as compared to the quantum resources
used in quantum computation. Our results clarify the assumptions made and the
conditions needed when using quantum oracles. Using the same assumptions on
oracles within the simulation framework we show that for some specific
algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no
advantage in terms of query complexity. This does not detract from the fact
that quantum query complexity provides examples of how a quantum computer can
be expected to behave, which in turn has proved useful for finding new quantum
algorithms outside of the oracle paradigm, where the most prominent example is
Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure
Bell Inequalities for Position Measurements
Bell inequalities for position measurements are derived using the bits of the
binary expansion of position-measurement results. Violations of these
inequalities are obtained from the output state of the Non-degenerate Optical
Parametric Amplifier.Comment: revtex4, 2 figure
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