18 research outputs found
Generalized self-testing and the security of the 6-state protocol
Self-tested quantum information processing provides a means for doing useful
information processing with untrusted quantum apparatus. Previous work was
limited to performing computations and protocols in real Hilbert spaces, which
is not a serious obstacle if one is only interested in final measurement
statistics being correct (for example, getting the correct factors of a large
number after running Shor's factoring algorithm). This limitation was shown by
McKague et al. to be fundamental, since there is no way to experimentally
distinguish any quantum experiment from a special simulation using states and
operators with only real coefficients.
In this paper, we show that one can still do a meaningful self-test of
quantum apparatus with complex amplitudes. In particular, we define a family of
simulations of quantum experiments, based on complex conjugation, with two
interesting properties. First, we are able to define a self-test which may be
passed only by states and operators that are equivalent to simulations within
the family. This extends work of Mayers and Yao and Magniez et al. in
self-testing of quantum apparatus, and includes a complex measurement. Second,
any of the simulations in the family may be used to implement a secure 6-state
QKD protocol, which was previously not known to be implementable in a
self-tested framework.Comment: To appear in proceedings of TQC 201
Quantum Cryptography Based Solely on Bell's Theorem
Information-theoretic key agreement is impossible to achieve from scratch and
must be based on some - ultimately physical - premise. In 2005, Barrett, Hardy,
and Kent showed that unconditional security can be obtained in principle based
on the impossibility of faster-than-light signaling; however, their protocol is
inefficient and cannot tolerate any noise. While their key-distribution scheme
uses quantum entanglement, its security only relies on the impossibility of
superluminal signaling, rather than the correctness and completeness of quantum
theory. In particular, the resulting security is device independent. Here we
introduce a new protocol which is efficient in terms of both classical and
quantum communication, and that can tolerate noise in the quantum channel. We
prove that it offers device-independent security under the sole assumption that
certain non-signaling conditions are satisfied. Our main insight is that the
XOR of a number of bits that are partially secret according to the
non-signaling conditions turns out to be highly secret. Note that similar
statements have been well-known in classical contexts. Earlier results had
indicated that amplification of such non-signaling-based privacy is impossible
to achieve if the non-signaling condition only holds between events on Alice's
and Bob's sides. Here, we show that the situation changes completely if such a
separation is given within each of the laboratories.Comment: 32 pages, v2: changed introduction, added reference
Graph-Theoretic Framework for Self-Testing in Bell Scenarios
Quantum self-testing is the task of certifying quantum states and
measurements using the output statistics solely, with minimal assumptions about
the underlying quantum system. It is based on the observation that some
extremal points in the set of quantum correlations can only be achieved, up to
isometries, with specific states and measurements. Here, we present a new
approach for quantum self-testing in Bell non-locality scenarios, motivated by
the following observation: the quantum maximum of a given Bell inequality is,
in general, difficult to characterize. However, it is strictly contained in an
easy-to-characterize set: the \emph{theta body} of a vertex-weighted induced
subgraph of the graph in which vertices represent the events and edges
join mutually exclusive events. This implies that, for the cases where the
quantum maximum and the maximum within the theta body (known as the Lov\'asz
theta number) of coincide, self-testing can be demonstrated by just
proving self-testability with the theta body of . This graph-theoretic
framework allows us to (i) recover the self-testability of several quantum
correlations that are known to permit self-testing (like those violating the
Clauser-Horne-Shimony-Holt (CHSH) and three-party Mermin Bell inequalities for
projective measurements of arbitrary rank, and chained Bell inequalities for
rank-one projective measurements), (ii) prove the self-testability of quantum
correlations that were not known using existing self-testing techniques (e.g.,
those violating the Abner Shimony Bell inequality for rank-one projective
measurements). Additionally, the analysis of the chained Bell inequalities
gives us a closed-form expression of the Lov\'asz theta number for a family of
well-studied graphs known as the M\"obius ladders, which might be of
independent interest in the community of discrete mathematics.Comment: 29 page