5,438 research outputs found
Causal order as a resource for quantum communication
In theories of communication, it is usually presumed that the involved
parties perform actions in a fixed causal order. However, practical and
fundamental reasons can induce uncertainties in the causal order. Here we show
that a maximal uncertainty in the causal order forbids asymptotic quantum
communication, while still enabling the noisy transfer of classical
information. Therefore causal order, like shared entanglement, is an additional
resource for communication. The result is formulated within an asymptotic
setting for processes with no fixed causal order, which sets a basis for a
quantum information theory in general quantum causal structures.Comment: 5 pages, 1 figur
Recommender Systems by means of Information Retrieval
In this paper we present a method for reformulating the Recommender Systems
problem in an Information Retrieval one. In our tests we have a dataset of
users who give ratings for some movies; we hide some values from the dataset,
and we try to predict them again using its remaining portion (the so-called
"leave-n-out approach"). In order to use an Information Retrieval algorithm, we
reformulate this Recommender Systems problem in this way: a user corresponds to
a document, a movie corresponds to a term, the active user (whose rating we
want to predict) plays the role of the query, and the ratings are used as
weigths, in place of the weighting schema of the original IR algorithm. The
output is the ranking list of the documents ("users") relevant for the query
("active user"). We use the ratings of these users, weighted according to the
rank, to predict the rating of the active user. We carry out the comparison by
means of a typical metric, namely the accuracy of the predictions returned by
the algorithm, and we compare this to the real ratings from users. In our first
tests, we use two different Information Retrieval algorithms: LSPR, a recently
proposed model based on Discrete Fourier Transform, and a simple vector space
model
Causation does not explain contextuality
Realist interpretations of quantum mechanics presuppose the existence of
elements of reality that are independent of the actions used to reveal them.
Such a view is challenged by several no-go theorems that show quantum
correlations cannot be explained by non-contextual ontological models, where
physical properties are assumed to exist prior to and independently of the act
of measurement. However, all such contextuality proofs assume a traditional
notion of causal structure, where causal influence flows from past to future
according to ordinary dynamical laws. This leaves open the question of whether
the apparent contextuality of quantum mechanics is simply the signature of some
exotic causal structure, where the future might affect the past or distant
systems might get correlated due to non-local constraints. Here we show that
quantum predictions require a deeper form of contextuality: even allowing for
arbitrary causal structure, no model can explain quantum correlations from
non-contextual ontological properties of the world, be they initial states,
dynamical laws, or global constraints.Comment: 18+8 pages, 3 figure
A quantum causal discovery algorithm
Finding a causal model for a set of classical variables is now a
well-established task---but what about the quantum equivalent? Even the notion
of a quantum causal model is controversial. Here, we present a causal discovery
algorithm for quantum systems. The input to the algorithm is a process matrix
describing correlations between quantum events. Its output consists of
different levels of information about the underlying causal model. Our
algorithm determines whether the process is causally ordered by grouping the
events into causally-ordered non-signaling sets. It detects if all relevant
common causes are included in the process, which we label Markovian, or
alternatively if some causal relations are mediated through some external
memory. For a Markovian process, it outputs a causal model, namely the causal
relations and the corresponding mechanisms, represented as quantum states and
channels. Our algorithm provides a first step towards more general methods for
quantum causal discovery.Comment: 11 pages, 10 figures, revised to match published versio
Renormalized entropy of entanglement in relativistic field theory
Entanglement is defined between subsystems of a quantum system, and at fixed
time two regions of space can be viewed as two subsystems of a relativistic
quantum field. The entropy of entanglement between such subsystems is
ill-defined unless an ultraviolet cutoff is introduced, but it still diverges
in the continuum limit. This behaviour is generic for arbitrary finite-energy
states, hence a conceptual tension with the finite entanglement entropy typical
of nonrelativistic quantum systems. We introduce a novel approach to explain
the transition from infinite to finite entanglement, based on coarse graining
the spatial resolution of the detectors measuring the field state. We show that
states with a finite number of particles become localized, allowing an
identification between a region of space and the nonrelativistic degrees of
freedom of the particles therein contained, and that the renormalized entropy
of finite-energy states reduces to the entanglement entropy of nonrelativistic
quantum mechanics.Comment: 5 pages, 1 figur
Updating the Born rule
Despite the tremendous empirical success of quantum theory there is still
widespread disagreement about what it can tell us about the nature of the
world. A central question is whether the theory is about our knowledge of
reality, or a direct statement about reality itself. Regardless of their stance
on this question, current interpretations of quantum theory regard the Born
rule as fundamental and add an independent state-update (or "collapse") rule to
describe how quantum states change upon measurement. In this paper we present
an alternative perspective and derive a probability rule that subsumes both the
Born rule and the collapse rule. We show that this more fundamental probability
rule can provide a rigorous foundation for informational, or "knowledge-based",
interpretations of quantum theory.Comment: 6+2 pages; 3 figure
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