57 research outputs found
Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
We present a technique for reducing the computational requirements by several
orders of magnitude in the evaluation of semidefinite relaxations for bounding
the set of quantum correlations arising from finite-dimensional Hilbert spaces.
The technique, which we make publicly available through a user-friendly
software package, relies on the exploitation of symmetries present in the
optimisation problem to reduce the number of variables and the block sizes in
semidefinite relaxations. It is widely applicable in problems encountered in
quantum information theory and enables computations that were previously too
demanding. We demonstrate its advantages and general applicability in several
physical problems. In particular, we use it to robustly certify the
non-projectiveness of high-dimensional measurements in a black-box scenario
based on self-tests of -dimensional symmetric informationally complete
POVMs.Comment: A. T. and D. R. contributed equally for this projec
Retreat from Intermediate Scrutiny in Gender-Based Discrimination Cases
Self-testing refers to the possibility of characterizing an unknown quantum device based only on the observed statistics. Here we develop methods for self-testing entangled quantum measurements, a key element for quantum networks. Our approach is based on the natural assumption that separated physical sources in a network should be considered independent. This provides a natural formulation of the problem of certifying entangled measurements. Considering the setup of entanglement swapping, we derive a robust self-test for the Bell-state measurement, tolerating noise levels up to 5%. We also discuss generalizations to other entangled measurements
Nonlocality under Computational Assumptions
Nonlocality and its connections to entanglement are fundamental features of
quantum mechanics that have found numerous applications in quantum information
science. A set of correlations is said to be nonlocal if it cannot be
reproduced by spacelike-separated parties sharing randomness and performing
local operations. An important practical consideration is that the runtime of
the parties has to be shorter than the time it takes light to travel between
them. One way to model this restriction is to assume that the parties are
computationally bounded. We therefore initiate the study of nonlocality under
computational assumptions and derive the following results:
(a) We define the set (not-efficiently-local) as consisting of
all bipartite states whose correlations arising from local measurements cannot
be reproduced with shared randomness and \emph{polynomial-time} local
operations.
(b) Under the assumption that the Learning With Errors problem cannot be
solved in \emph{quantum} polynomial-time, we show that
, where is the set of \emph{all}
bipartite entangled states (pure and mixed). This is in contrast to the
standard notion of nonlocality where it is known that some entangled states,
e.g. Werner states, are local. In essence, we show that there exist (efficient)
local measurements producing correlations that cannot be reproduced through
shared randomness and quantum polynomial-time computation.
(c) We prove that if unconditionally, then
. In other words, the ability to certify all
bipartite entangled states against computationally bounded adversaries gives a
non-trivial separation of complexity classes.
(d) Using (c), we show that a certain natural class of 1-round delegated
quantum computation protocols that are sound against provers
cannot exist.Comment: 65 page
Limits on correlations in networks for quantum and no-signaling resources
A quantum network consists of independent sources distributing entangled
states to distant nodes which can then perform entangled measurements, thus
establishing correlations across the entire network. But how strong can these
correlations be? Here we address this question, by deriving bounds on possible
quantum correlations in a given network. These bounds are nonlinear
inequalities that depend only on the topology of the network. We discuss in
detail the notably challenging case of the triangle network. Moreover, we
conjecture that our bounds hold in general no-signaling theories. In
particular, we prove that our inequalities for the triangle network hold when
the sources are arbitrary no-signaling boxes which can be wired together.
Finally, we discuss an application of our results for the device-independent
characterization of the topology of a quantum network.Comment: 15 pages, 6 figure
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
No distributed quantum advantage for approximate graph coloring
We give an almost complete characterization of the hardness of -coloring
-chromatic graphs with distributed algorithms, for a wide range of models
of distributed computing. In particular, we show that these problems do not
admit any distributed quantum advantage. To do that: 1) We give a new
distributed algorithm that finds a -coloring in -chromatic graphs in
rounds, with . 2) We prove that any distributed
algorithm for this problem requires rounds.
Our upper bound holds in the classical, deterministic LOCAL model, while the
near-matching lower bound holds in the non-signaling model. This model,
introduced by Arfaoui and Fraigniaud in 2014, captures all models of
distributed graph algorithms that obey physical causality; this includes not
only classical deterministic LOCAL and randomized LOCAL but also quantum-LOCAL,
even with a pre-shared quantum state.
We also show that similar arguments can be used to prove that, e.g.,
3-coloring 2-dimensional grids or -coloring trees remain hard problems even
for the non-signaling model, and in particular do not admit any quantum
advantage. Our lower-bound arguments are purely graph-theoretic at heart; no
background on quantum information theory is needed to establish the proofs
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