248 research outputs found
Information and communication in polygon theories
Generalized probabilistic theories (GPT) provide a framework in which one can
formulate physical theories that includes classical and quantum theories, but
also many other alternative theories. In order to compare different GPTs, we
advocate an approach in which one views a state in a GPT as a resource, and
quantifies the cost of interconverting between different such resources. We
illustrate this approach on polygon theories (Janotta et al. New J. Phys 13,
063024, 2011) that interpolate (as the number n of edges of the polygon
increases) between a classical trit (when n=3) and a real quantum bit (when
n=infinity). Our main results are that simulating the transmission of a single
n-gon state requires more than one qubit, or more than log(log(n)) bits, and
that n-gon states with n odd cannot be simulated by n'-gon states with n' even
(for all n,n'). These results are obtained by showing that the classical
capacity of a single n-gon state with n even is 1 bit, whereas it is larger
than 1 bit when n is odd; by showing that transmitting a single n-gon state
with n even violates information causality; and by showing studying the
communication complexity cost of the nondeterministic not equal function using
n-gon states.Comment: 18 page
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
Optimal Quantum Cloning Machines
We present Quantum Cloning Machines (QCM) that transform N identical qubits
into identical copies and we prove that the fidelity (quality) of these
copies is optimal. The connection between cloning and measurement is discussed
in detail. When the number of clones M tends towards infinity, the fidelity of
each clone tends towards the optimal fidelity that can be obtained by a
measurement on the input qubits. More generally, the QCM are universal devices
to translate quantum information into classical information.Comment: 4 pages, Latex, 1 postscript figure, (very) minor modification
No-Flipping as a consequence of No-Signalling and Non-increase of Entanglement under LOCC
Non existence of Universal NOT gate for arbitrary quantum mechanical states
is a fundamental constraint on the allowed operations performed on physical
systems. The largest set of states that can be flipped by using a single NOT
gate is the set of states lying on a great circle of the Bloch-sphere. In this
paper, we show the impossibility of universal exact-flipping operation, first
by using the fact that no faster than light communication is possible and then
by using the principle of "non-increase of entanglement under LOCC".
Interestingly, exact flipping of the states of any great circle does not
violate these two principles, as expected.Comment: 8 pages, published versio
Frequency Bin Entangled Photons
A monochromatic laser pumping a parametric down conversion crystal generates
frequency entangled photon pairs. We study this experimentally by addressing
such frequency entangled photons at telecommunication wavelengths (around 1550
nm) with fiber optics components such as electro-optic phase modulators and
narrow band frequency filters. The theory underlying our approach is developed
by introducing the notion of frequency bin entanglement. Our results show that
the phase modulators address coherently up to eleven frequency bins, leading to
an interference pattern which can violate a Bell inequality adapted to our
setup by more than five standard deviations.Comment: 10 pages, 4 figures (extended version
Optimal universal quantum cloning and state estimation
We derive a tight upper bound for the fidelity of a universal N to M qubit
cloner, valid for any M \geq N, where the output of the cloner is required to
be supported on the symmetric subspace. Our proof is based on the concatenation
of two cloners and the connection between quantum cloning and quantum state
estimation. We generalise the operation of a quantum cloner to mixed and/or
entangled input qubits described by a density matrix supported on the symmetric
subspace of the constituent qubits. We also extend the validity of optimal
state estimation methods to inputs of this kind.Comment: 4 pages (RevTeX
Source Vacuum Fluctuations of Black Hole Radiance
The emergence of Hawking radiation from vacuum fluctuations is analyzed in
conventional field theories and their energy content is defined through the
Aharonov weak value concept. These fluctuations travel in flat space-time and
carry transplanckian energies sharply localized on cisplanckian distances. We
argue that these features cannot accommodate gravitational nonlinearities. We
suggest that the very emission of Hawking photons from tamed vacuum
fluctuations requires the existence of an exploding set of massive fields.
These considerations corroborate some conjectures of Susskind and may prove
relevant for the back-reaction problem and for the unitarity issue.Comment: 33 pages, ULB-TH 03/94, 5 figures not included, available on request
from F.E. (problem with truncation of long lines
Quantum coin tossing and bit-string generation in the presence of noise
We discuss the security implications of noise for quantum coin tossing
protocols. We find that if quantum error correction can be used, so that noise
levels can be made arbitrarily small, then reasonable security conditions for
coin tossing can be framed so that results from the noiseless case will
continue to hold. If, however, error correction is not available (as is the
case with present day technology), and significant noise is present, then
tossing a single coin becomes problematic. In this case, we are led to consider
random n-bit string generation in the presence of noise, rather than
single-shot coin tossing. We introduce precise security criteria for n-bit
string generation and describe an explicit protocol that could be implemented
with present day technology. In general, a cheater can exploit noise in order
to bias coins to their advantage. We derive explicit upper bounds on the
average bias achievable by a cheater for given noise levels.Comment: REVTeX. 6 pages, no figures. Early versions contained errors in
statements of security conditions, although results were correct. v4: PRA
versio
Extremal equation for optimal completely-positive maps
We derive an extremal equation for optimal completely-positive map which most
closely approximates a given transformation between pure quantum states.
Moreover, we also obtain an upper bound on the maximal mean fidelity that can
be attained by the optimal approximate transformation. The developed formalism
is applied to universal-NOT gate, quantum cloning machines, quantum entanglers,
and qubit theta-shifter.Comment: REVTeX, 7 pages, 2 figures, important reference adde
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