19 research outputs found
Monogamy relations for relativistically causal correlations
Non-signalling conditions encode minimal requirements that any (quantum)
systems put into spatial arrangements must satisfy in order to be consistent
with special relativity. Recent works have argued that in scenarios involving
more that two parties, conditions compatible with relativistic causality do not
have to satisfy all possible non-signalling conditions but only a subset of
them. Here we show that correlations satisfying only this subset of constraints
have to satisfy highly non-local monogamy relations between the effects of
space-like separated random variables. These monogamy relations take the form
of new entropic inequalities between the various systems and we give a general
method to derive them. Using these monogamy relations we refute previous
suggestions for physical mechanisms that could lead to relativistically causal
correlations, demonstrating that such mechanisms would lead to superluminal
signalling.Comment: 14 pages, 4 figure
Toward correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game
Correlation self-testing of a theory addresses the question of whether we can
identify the set of correlations realisable in a theory from its performance in
a particular information processing task. Applied to quantum theory it aims to
identify an information processing task whose optimal performance is achieved
only by theories realising the same correlations as quantum theory in any
causal structure. In [Phys. Rev. Lett. 125 060406 (2020)] we introduced a
candidate task for this, the adaptive CHSH game. Here, we analyse the maximum
probability of winning this game in different generalised probabilistic
theories. We show that theories with a joint state space given by the minimal
or the maximal tensor product are inferior to quantum theory, before
considering other tensor products in theories whose elementary systems have
various two-dimensional state spaces. For these, we find no theories that
outperform quantum theory in the adaptive CHSH game and prove that it is
impossible to recover the quantum performance in various cases. This is the
first step towards a general solution that, if successful, will have
wide-ranging consequences, in particular, enabling an experiment that could
rule out all theories in which the set of realisable correlations does not
coincide with the quantum set.Comment: 12+2 pages, 2 figures; v2: typos correcte
Analysing causal structures in generalised probabilistic theories
Causal structures give us a way to understand the origin of observed
correlations. These were developed for classical scenarios, but quantum
mechanical experiments necessitate their generalisation. Here we study causal
structures in a broad range of theories, which include both quantum and
classical theory as special cases. We propose a method for analysing
differences between such theories based on the so-called measurement entropy.
We apply this method to several causal structures, deriving new relations that
separate classical, quantum and more general theories within these causal
structures. The constraints we derive for the most general theories are in a
sense minimal requirements of any causal explanation in these scenarios. In
addition, we make several technical contributions that give insight for the
entropic analysis of quantum causal structures. In particular, we prove that
for any causal structure and for any generalised probabilistic theory, the set
of achievable entropy vectors form a convex cone.Comment: 11+13 pages, 5 figures, v2: new examples and additional discussion
added, v3 (published version): presentation improve
Quantum Causal Structure and Quantum Thermodynamics
This thesis reports progress in two domains, namely causal structures and microscopic thermodynamics, both of which are highly pertinent in the development of quantum technologies. Causal structures fundamentally influence the development of protocols for quantum cryptography and microscopic thermodynamics is crucial for the design of quantum computers.
The first part is dedicated to the analysis of causal structure, which encodes the relationship between observed variables, in general restricting the set of possible correlations between them. Our considerations rely on a recent entropy vector method, which we first review. We then develop new techniques for deriving entropic constraints to differentiate between causal structures. We provide sufficient conditions for entropy vectors to be realisable within a causal structure and derive new, improved necessary conditions in terms of so-called non-Shannon inequalities. We also report that for a family of causal structures, including the bipartite Bell scenario and the bilocal causal structure, entropy vectors are unable to distinguish between classical and quantum causes, in spite of the existence of quantum correlations that are not classically reproducible. Hence, further development is needed in order to understand cause from a quantum perspective.
In the second part we explore an axiomatic framework for modelling error-tolerant processes in microscopic thermodynamics. Our axiomatisation allows for the accommodation of finite precision levels, which is crucial for describing experiments in the microscopic regime. Moreover, it is general enough to permit the consideration of different error types. The framework leads to the emergence of manageable quantities that give insights into the feasibility and expenditure of processes, which for adiabatic processes are shown to be smooth entropy measures. Our framework also leads to thermodynamic behaviour at the macroscopic scale, meaning that for thermodynamic equilibrium states a unique function provides necessary and sufficient conditions for state transformations, like in the traditional second law
Non-Shannon inequalities in the entropy vector approach to causal structures
A causal structure is a relationship between observed variables that in
general restricts the possible correlations between them. This relationship can
be mediated by unobserved systems, modelled by random variables in the
classical case or joint quantum systems in the quantum case. One way to
differentiate between the correlations realisable by two different causal
structures is to use entropy vectors, i.e., vectors whose components correspond
to the entropies of each subset of the observed variables. To date, the
starting point for deriving entropic constraints within causal structures are
the so-called Shannon inequalities (positivity of entropy, conditional entropy
and conditional mutual information). In the present work we investigate what
happens when non-Shannon entropic inequalities are included as well. We show
that in general these lead to tighter outer approximations of the set of
realisable entropy vectors and hence enable a sharper distinction of different
causal structures. Since non-Shannon inequalities can only be applied amongst
classical variables, it might be expected that their use enables an entropic
distinction between classical and quantum causal structures. However, this
remains an open question. We also introduce techniques for deriving inner
approximations to the allowed sets of entropy vectors for a given causal
structure. These are useful for proving tightness of outer approximations or
for finding interesting regions of entropy space. We illustrate these
techniques in several scenarios, including the triangle causal structure.Comment: 23 pages + appendix; v2: minor changes to Section IV A; v3: paper has
been significantly shortened, an expanded version of the removed review
section can be found in arXiv:1709.08988; v4: version to be published,
supplementary information available as ancillary file
Smooth entropy in axiomatic thermodynamics
Thermodynamics can be formulated in either of two approaches, the
phenomenological approach, which refers to the macroscopic properties of
systems, and the statistical approach, which describes systems in terms of
their microscopic constituents. We establish a connection between these two
approaches by means of a new axiomatic framework that can take errors and
imprecisions into account. This link extends to systems of arbitrary sizes
including microscopic systems, for which the treatment of imprecisions is
pertinent to any realistic situation. Based on this, we identify the quantities
that characterise whether certain thermodynamic processes are possible with
entropy measures from information theory. In the error-tolerant case, these
entropies are so-called smooth min and max entropies. Our considerations
further show that in an appropriate macroscopic limit there is a single entropy
measure that characterises which state transformations are possible. In the
case of many independent copies of a system (the so-called i.i.d. regime), the
relevant quantity is the von Neumann entropy.Comment: 18 pages, 1 figure; book chapter in "Thermodynamics in the Quantum
Regime - Recent Progress and Outlook", eds. F. Binder, L. A. Correa, C.
Gogolin, J. Anders and G. Adesso; the chapter relies on results reported in
MW's PhD thesis, arXiv:1807.0634
Self-Testing of Physical Theories, or, Is Quantum Theory Optimal with Respect to Some Information-Processing Task?
Self-testing usually refers to the task of taking a given set of observed
correlations that are assumed to arise via a process that is accurately
described by quantum theory, and trying to infer the quantum state and
measurements. In other words it is concerned with the question of whether we
can tell what quantum black-box devices are doing by looking only at their
input-output behaviour and is known to be possible in several cases. Here we
introduce a more general question: is it possible to self-test a theory, and,
in particular, quantum theory? More precisely, we ask whether within a
particular causal structure there are tasks that can only be performed in
theories that have the same correlations as quantum mechanics in any scenario.
We present a candidate task for such a correlation self-test and analyse it in
a range of generalised probabilistic theories (GPTs), showing that none of
these perform better than quantum theory. A generalisation of our results
showing that all non-quantum GPTs are strictly inferior to quantum mechanics
for this task would point to a new way to axiomatise quantum theory, and enable
an experimental test that simultaneously rules out such GPTs.Comment: 6 pages; v2: close to published version; v3: typos correcte
Multisystem measurements in generalized probabilistic theories and their role in information processing
Generalized probabilistic theories (GPTs) provide a framework in which a
range of possible theories can be examined, including classical theory, quantum
theory and those beyond. In general, enlarging the state space of a GPT leads
to fewer possible measurements because the additional states give stronger
constraints on the set of effects, the constituents of measurements. This can
have implications for information processing. In boxworld, for example, a GPT
in which any no-signalling distribution can be realised, there is no analogue
of a measurement in the Bell basis and hence the analogue of entanglement
swapping is impossible. A comprehensive study of measurements on multiple
systems in boxworld has been lacking. Here we consider such measurements in
detail, distinguishing those that can be performed by interacting with
individual systems sequentially (termed wirings), and the more interesting set
of those that cannot. We compute all the possible boxworld effects for cases
with small numbers of inputs, outputs and parties, identifying those that are
wirings. The large state space of boxworld leads to a small effect space and
hence the effects of boxworld are widely applicable in GPTs. We also show some
possible uses of non-wirings for information processing by studying state
discrimination, nonlocality distillation and the boxworld analogue of
nonlocality without entanglement. Finally, we connect our results to the study
of logically consistent classical processes and to the composition of
contextuality scenarios. By enhancing understanding of measurements in
boxworld, our results could be useful in studies of possible underlying
principles on which quantum theory can be based.Comment: 17 pages, 3 figures; v2: application to nonlocality without
entanglement added v3: new title and other updates to match published versio
Quantum physics needs complex numbers
Complex numbers, i.e., numbers with a real and an imaginary part, are
essential for mathematical analysis, while their role in other subjects, such
as electromagnetism or special relativity, is far less fundamental. Quantum
physics is the only physical theory where these numbers seem to play an
indispensible role, as the theory is explicitly formulated in terms of
operators acting on complex Hilbert spaces. The occurrence of complex numbers
within the quantum formalism has nonetheless puzzled countless physicists,
including the fathers of the theory, for whom a real version of quantum
physics, where states and observables are represented by real operators, seemed
much more natural. In fact, previous works showed that such "real quantum
physics" can reproduce the outcomes of any multipartite experiment, as long as
the parts share arbitrary real quantum states. Thus, are complex numbers really
needed for a quantum description of nature? Here, we show this to be case by
proving that real and complex quantum physics make different predictions in
network scenarios comprising independent quantum state sources. This allows us
to devise a Bell-type quantum experiment whose input-output correlations cannot
be approximated by any real quantum model. The successful realization of such
an experiment would disprove real quantum physics, in the same way as standard
Bell experiments disproved local physics.Comment: 17 pages. MATLAB codes available under reques
Inability of the entropy vector method to certify nonclassicality in linelike causal structures
Bell's theorem shows that our intuitive understanding of causation must be
overturned in light of quantum correlations. Nevertheless, quantum mechanics
does not permit signalling and hence a notion of cause remains. Understanding
this notion is not only important at a fundamental level, but also for
technological applications such as key distribution and randomness expansion.
It has recently been shown that a useful way to decide which classical causal
structures could give rise to a given set of correlations is to use entropy
vectors. These are vectors whose components are the entropies of all subsets of
the observed variables in the causal structure. The entropy vector method
employs causal relationships among the variables to restrict the set of
possible entropy vectors. Here, we consider whether the same approach can lead
to useful certificates of non-classicality within a given causal structure.
Surprisingly, we find that for a family of causal structures that include the
usual bipartite Bell structure they do not. For all members of this family, no
function of the entropies of the observed variables gives such a certificate,
in spite of the existence of nonclassical correlations. It is therefore
necessary to look beyond entropy vectors to understand cause from a quantum
perspective.Comment: 5 pages + appendix, v2: added references, v3: new title, added
journal referenc