39 research outputs found
Stronger Quantum Correlations with Loophole-free Post-selection
One of the most striking non-classical features of quantum mechanics is in
the correlations it predicts between spatially separated measurements. In local
hidden variable theories, correlations are constrained by Bell inequalities,
but quantum correlations violate these. However, experimental imperfections
lead to "loopholes" whereby LHV correlations are no longer constrained by Bell
inequalities, and violations can be described by LHV theories. For example,
loopholes can emerge through selective detection of events. In this letter, we
introduce a clean, operational picture of multi-party Bell tests, and show that
there exists a non-trivial form of loophole-free post-selection. Surprisingly,
the same post-selection can enhance quantum correlations, and unlock a
connection between non-classical correlations and non-classical computation.Comment: 4 pages, 2 figures, substantially revised in response to referee
suggestion
Computational Perspectives on Bell Inequalities and Many-body Quantum Correlations
The predictions of quantum mechanics cannot be resolved with a completely
classical view of the world. In particular, the statistics of space-like
separated measurements on entangled quantum systems violate a Bell inequality.
We put forward a computational perspective on a broad class of Bell tests that
study correlators, or the statistics of joint measurement outcomes. We
associate particular maps, or functions to particular theories. The violation
of a Bell inequality then implies the ability to perform some functions, or
computations that classical, or more generally, local hidden variable (LHV)
theories cannot.Comment: PhD thesis: 169 pages, 3 figures, and hopefully is of use to someon
Almost quantum correlations
There have been a number of attempts to derive the set of quantum non-local
correlations from reasonable physical principles. Here we introduce
, a set of multipartite supra-quantum correlations that has appeared
under different names in fields as diverse as graph theory, quantum gravity and
quantum information science. We argue that may correspond to the
set of correlations of a reasonable physical theory, in which case the research
program to reconstruct quantum theory from device-independent principles is met
with strong obstacles. In support of this conjecture, we prove that
is closed under classical operations and satisfies the physical principles of
Non-Trivial Communication Complexity, No Advantage for Nonlocal Computation,
Macroscopic Locality and Local Orthogonality. We also review numerical evidence
that almost quantum correlations satisfy Information Causality.Comment: 15+2 pages, 1 figur
Bipartite Postquantum Steering in Generalized Scenarios
The study of stronger-than-quantum effects is a fruitful line of research that provides valuable insight into quantum theory. Unfortunately, traditional bipartite steering scenarios can always be explained by quantum theory. Here, we show that, by relaxing this traditional setup, bipartite steering incompatible with quantum theory is possible. The two scenarios we describe, which still feature Alice remotely steering Bobâs system, are (i) one where Bob also has an input and operates on his subsystem, and (ii) the âinstrumental steeringâ scenario. We show that such bipartite postquantum steering is a genuinely new type of postquantum nonlocality, which does not follow from postquantum Bell nonlocality. In addition, we present a method to bound quantum violations of steering inequalities in these scenarios
Complexity of compatible measurements
Measurement incompatibility is one of the basic aspects of quantum theory. Here we study the structure of the set of compatible, i.e., jointly measurable, measurements. We are interested in whether or not there exist compatible measurements whose parent is maximally complex, in the sense of requiring a number of outcomes exponential in the number of measurements, and related questions. Although we show this to be the case in a number of simple scenarios, we show that generically it cannot happen, by proving an upper bound on the number of outcomes of a parent measurement that is linear in the number of compatible measurements. We discuss why this does not trivialize the problem of finding parent measurements, but rather shows that a trade-off between memory and time can be achieved. Finally, we also investigate the complexity of extremal compatible measurements in regimes where our bound is not tight and uncover rich structure
Self-testing and certification using trusted quantum inputs
Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows from Bell non-locality. There exist other scenarios, known as semi-device-independent, in which assumptions are made on the devices, such as their dimension, and non-classicality is associated to the observation of other types of correlations with no classical analogue. More recently, the use of trusted quantum inputs for certification has been introduced. The goal of this work is to study the power of this formalism and describe self-testing protocols in various settings using trusted quantum inputs. We also relate these different types of self-testing to some of the most basic quantum information protocols, such as quantum teleportation. Finally, we apply our findings to quantum networks and provide methods for estimating the quality of the whole network, as well as of parts of it
One-Sided Device-Independent Certification of Unbounded Random Numbers
The intrinsic non-locality of correlations in Quantum Mechanics allow us to
certify the behaviour of a quantum mechanism in a device independent way. In
particular, we present a new protocol that allows an unbounded amount of
randomness to be certified as being legitimately the consequence of a
measurement on a quantum state. By using a sequence of non-projective
measurements on single state, we show a more robust method to certify unbounded
randomness than the protocol of Churchod et al., by moving to a one-sided
device independent scenario. This protocol also does not assume any specific
behaviour of the adversary trying to fool the participants in the protocol,
which is an advantage over previous steering based protocols. We present
numerical results which confirm the optimal functioning of this protocol in the
ideal case. Furthermore, we also study an experimental scenario to determine
the feasibility of the protocol in a realistic implementation. The effect of
depolarizing noise is examined, by studying a potential state produced by a
networked system of ion traps.Comment: In Proceedings PC 2018, arXiv:1807.1056