84 research outputs found
Resetting uncontrolled quantum systems
We consider a scenario where we wish to bring a closed system of known
Hilbert space dimension (the target), subject to an unknown Hamiltonian
evolution, back to its quantum state at a past time . The target is out of
our control: this means that we ignore both its free Hamiltonian and how the
system interacts with other quantum systems we may use to influence it. Under
these conditions, we prove that there exist protocols within the framework of
non-relativistic quantum physics which reset the target system to its exact
quantum state at . Each "resetting protocol" is successful with non-zero
probability for all possible free Hamiltonians and interaction unitaries, save
a subset of zero measure. When the target is a qubit and the interaction is
sampled from the Haar measure, the simplest resetting circuits have a
significant average probability of success and their implementation is within
reach of current quantum technologies. Finally, we find that, in case the
resetting protocol fails, it is possible to run a further protocol that, if
successful, undoes both the natural evolution of the target and the effects of
the failed protocol over the latter. By chaining in this fashion several such
protocols, one can substantially increase the overall probability of a
successful resetting.Comment: Published version. This work was not funded by the European Research
Counci
Security bounds for continuous variables quantum key distribution
Security bounds for key distribution protocols using coherent and squeezed
states and homodyne measurements are presented. These bounds refer to (i)
general attacks and (ii) collective attacks where Eve interacts individually
with the sent states, but delays her measurement until the end of the
reconciliation process. For the case of a lossy line and coherent states, it is
first proven that a secure key distribution is possible up to 1.9 dB of losses.
For the second scenario, the security bounds are the same as for the completely
incoherent attack.Comment: See also F. Grosshans, quant-ph/040714
Bond dimension witnesses and the structure of homogeneous matrix product states
For the past twenty years, Matrix Product States (MPS) have been widely used
in solid state physics to approximate the ground state of one-dimensional spin
chains. In this paper, we study homogeneous MPS (hMPS), or MPS constructed via
site-independent tensors and a boundary condition. Exploiting a connection with
the theory of matrix algebras, we derive two structural properties shared by
all hMPS, namely: a) there exist local operators which annihilate all hMPS of a
given bond dimension; and b) there exist local operators which, when applied
over any hMPS of a given bond dimension, decouple (cut) the particles where
they act from the spin chain while at the same time join (glue) the two loose
ends back again into a hMPS. Armed with these tools, we show how to
systematically derive `bond dimension witnesses', or 2-local operators whose
expectation value allows us to lower bound the bond dimension of the underlying
hMPS. We extend some of these results to the ansatz of Projected Entangled
Pairs States (PEPS). As a bonus, we use our insight on the structure of hMPS
to: a) derive some theoretical limitations on the use of hMPS and hPEPS for
ground state energy computations; b) show how to decrease the complexity and
boost the speed of convergence of the semidefinite programming hierarchies
described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of
finite-dimensional quantum correlations.Comment: Accepted for publication in Quantum. We still do not acknowledge
support from the European Research Counci
Gaussian Operations and Privacy
We consider the possibilities offered by Gaussian states and operations for
two honest parties, Alice and Bob, to obtain privacy against a third
eavesdropping party, Eve. We first extend the security analysis of the protocol
proposed in M. Navascues et al., Phys. Rev. Lett. 94, 010502 (2005). Then, we
prove that a generalized version of this protocol does not allow to distill a
secret key out of bound entangled Gaussian states
Theoretical research without projects
We propose a funding scheme for theoretical research that does not rely on
project proposals, but on recent past scientific productivity. Given a
quantitative figure of merit on the latter and the total research budget, we
introduce a number of policies to decide the allocation of funds in each grant
call. Under some assumptions on scientific productivity, some of such policies
are shown to converge, in the limit of many grant calls, to a funding
configuration that is close to the maximum total productivity of the whole
scientific community. We present numerical simulations showing evidence that
these schemes would also perform well in the presence of statistical noise in
the scientific productivity and/or its evaluation. Finally, we prove that one
of our policies cannot be cheated by individual research units. Our work must
be understood as a first step towards a mathematical theory of the research
activity.Comment: Some edits to the published versio
The Inflation Technique Completely Solves the Causal Compatibility Problem
The causal compatibility question asks whether a given causal structure graph
-- possibly involving latent variables -- constitutes a genuinely plausible
causal explanation for a given probability distribution over the graph's
observed variables. Algorithms predicated on merely necessary constraints for
causal compatibility typically suffer from false negatives, i.e. they admit
incompatible distributions as apparently compatible with the given graph. In
[arXiv:1609.00672], one of us introduced the inflation technique for
formulating useful relaxations of the causal compatibility problem in terms of
linear programming. In this work, we develop a formal hierarchy of such causal
compatibility relaxations. We prove that inflation is asymptotically tight,
i.e., that the hierarchy converges to a zero-error test for causal
compatibility. In this sense, the inflation technique fulfills a longstanding
desideratum in the field of causal inference. We quantify the rate of
convergence by showing that any distribution which passes the -order
inflation test must be -close in Euclidean norm to some
distribution genuinely compatible with the given causal structure. Furthermore,
we show that for many causal structures, the (unrelaxed) causal compatibility
problem is faithfully formulated already by either the first or second order
inflation test.Comment: Updated to match forthcoming journal publication as closely as
possible. Some content removed for brevity. Expanded citations. Most
footnotes moved into the main text. Significant changes to subsection 4.1,
where we corrected an error in the example of second order inflation not
converging, and added an converse example where second order inflation
outperforms other technique
How energy conservation limits our measurements
Observations in Quantum Mechanics are subject to complex restrictions arising
from the principle of energy conservation. Determining such restrictions,
however, has been so far an elusive task, and only partial results are known.
In this paper we discuss how constraints on the energy spectrum of a
measurement device translate into limitations on the measurements which we can
effect on a target system with non-trivial energy operator. We provide
efficient algorithms to characterize such limitations and we quantify them
exactly when the target is a two-level quantum system. Our work thus identifies
the boundaries between what is possible or impossible to measure, i.e., between
what we can see or not, when energy conservation is at stake.Comment: Better read the 5-page published version firs
Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
Self testing is a device independent approach to estimate the state and
measurement operators, without the need to assume the dimension of our quantum
system. In this paper, we show that one can self test black boxes into any pure
entangled two-qubit state, by performing simple Bell type experiments. The
approach makes use of only one family of two-inputs/two-outputs Bell
inequalities. Furthermore, we outline the sufficient conditions for one to self
test any dimensional bipartite entangled state. All these methods are robust to
small but inevitable experimental errors.Comment: 14 pages, 3 figure
Closed sets of correlations: answers from the zoo
We investigate the conditions under which a set of multipartite nonlocal
correlations can describe the distributions achievable by distant parties
conducting experiments in a consistent universe. Several questions are posed,
such as: are all such sets "nested", i.e., contained into one another? Are they
discrete or do they form a continuum? How many of them are supraquantum? Are
there non-trivial polytopes among them? We answer some of these questions or
relate them with established conjectures in complexity theory by introducing a
"zoo" of physically consistent sets which can be characterized efficiently via
either linear or semidefinite programming. As a bonus, we use the zoo to
derive, for the first time, concrete impossibility results in nonlocality
distillation.Comment: 24 pages, 5 figure
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