12 research outputs found
Qutrit witness from the Grothendieck constant of order four
In this paper, we prove that , where denotes the
Grothendieck constant of order . To this end, we use a branch-and-bound
algorithm commonly used in the solution of NP-hard problems. It has recently
been proven that . Here we prove that ,
which has implications for device-independent witnessing dimensions greater
than two. Furthermore, the algorithm with some modifications may find
applications in various black-box quantum information tasks with large number
of inputs and outputs.Comment: 13 pages, 2 figure
Bounding the persistency of the nonlocality of W states
The nonlocal properties of the W states are investigated under particle loss.
By removing all but two particles from an -qubit W state, the resulting
two-qubit state is still entangled. Hence, the W state has high persistency of
entanglement. We ask an analogous question regarding the persistency of
nonlocality introduced in [Phys. Rev. A 86, 042113]. Namely, we inquire what is
the minimal number of particles that must be removed from the W state so that
the resulting state becomes local. We bound this value in function of
qubits by considering Bell nonlocality tests with two alternative settings per
site. In particular, we find that this value is between and for
large . We also develop a framework to establish bounds for more than two
settings per site.Comment: 10 pages, 4 figure
Beating one bit of communication with and without quantum pseudo-telepathy
According to Bell's theorem, certain entangled states cannot be simulated
classically using local hidden variables (LHV). But if can we augment LHV by
classical communication, how many bits are needed to simulate them? There is a
strong evidence that a single bit of communication is powerful enough to
simulate projective measurements on any two-qubit entangled state. In this
study, we present Bell-like scenarios where bipartite correlations resulting
from projective measurements on higher dimensional states cannot be simulated
with a single bit of communication. These include a three-input, a four-input,
a seven-input, and a 63-input bipartite Bell-like inequality with 80089, 64,
16, and 2 outputs, respectively. Two copies of emblematic Bell expressions,
such as the Magic square pseudo-telepathy game, prove to be particularly
powerful, requiring a state to beat the one-bit classical bound,
and look a promising candidate for implementation on an optical platform.Comment: 11 pages, 4 table
1 Summary Substructural Functional Programming
Graph rewriting is a suitable technique to implement lazy functional languages efficiently.[1] A computation in a graph rewrite system is specified by a set of graph rewrite rules that are used to rewrite a given initial graph to its final result. The intermediate graphs are called data graphs. Consider the following facts: – Functional expressions can express any data graph. – During graph rewriting cyclic structures are preserved. More precisely: if two arcs in the data graph point to the same node A, they will point to the same node B until they will be garbage-collected (A and B might be the same). This could be a background for efficient implementation of graph algorithms, but at least two features are missing: – An expression should be able to distinguish that two arcs in the graph point to the same node or not. This is the comparing feature. – Suppose that we would like to alter a graph a little bit, and we know that the old value will not be used any more. In this case the graph could be destructively update
A funkcionális programozás tanulásának támogatása interaktĂv tanulássegĂtĹ‘ eszközökkel
Certification of qubits in the prepare-and-measure scenario with large input alphabet and connections with the Grothendieck constant
Abstract We address the problem of testing the quantumness of two-dimensional systems in the prepare-and-measure (PM) scenario, using a large number of preparations and a large number of measurement settings, with binary outcome measurements. In this scenario, we introduce constants, which we relate to the Grothendieck constant of order 3. We associate them with the white noise resistance of the prepared qubits and to the critical detection efficiency of the measurements performed. Large-scale numerical tools are used to bound the constants. This allows us to obtain new bounds on the minimum detection efficiency that a setup with 70 preparations and 70 measurement settings can tolerate