36 research outputs found
Quantum non-malleability and authentication
In encryption, non-malleability is a highly desirable property: it ensures
that adversaries cannot manipulate the plaintext by acting on the ciphertext.
Ambainis, Bouda and Winter gave a definition of non-malleability for the
encryption of quantum data. In this work, we show that this definition is too
weak, as it allows adversaries to "inject" plaintexts of their choice into the
ciphertext. We give a new definition of quantum non-malleability which resolves
this problem. Our definition is expressed in terms of entropic quantities,
considers stronger adversaries, and does not assume secrecy. Rather, we prove
that quantum non-malleability implies secrecy; this is in stark contrast to the
classical setting, where the two properties are completely independent. For
unitary schemes, our notion of non-malleability is equivalent to encryption
with a two-design (and hence also to the definition of Ambainis et al.). Our
techniques also yield new results regarding the closely-related task of quantum
authentication. We show that "total authentication" (a notion recently proposed
by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant
improvement over the eight-design construction of Garg et al. We also show
that, under a mild adaptation of the rejection procedure, both total
authentication and our notion of non-malleability yield quantum authentication
as defined by Dupuis, Nielsen and Salvail.Comment: 20+13 pages, one figure. v2: published version plus extra material.
v3: references added and update
Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory
Einstein introduced the locality principle which states that all physical
effect in some finite space-time region does not influence its space-like
separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei
captured the idea of the locality principle by the notion of operational
separability. The operation in operational separability is performed in some
finite space-time region, and leaves unchanged the state in its space-like
separated finite space-time region. This operation is defined with a completely
positive map. In the present paper, we justify using a completely positive map
as a local operation in algebraic quantum field theory, and show that this
local operation can be approximately written with Kraus operators under the
funnel property
Analysing causal structures with entropy
A central question for causal inference is to decide whether a set of
correlations fit a given causal structure. In general, this decision problem is
computationally infeasible and hence several approaches have emerged that look
for certificates of compatibility. Here we review several such approaches based
on entropy. We bring together the key aspects of these entropic techniques with
unified terminology, filling several gaps and establishing new connections
regarding their relation, all illustrated with examples. We consider cases
where unobserved causes are classical, quantum and post-quantum and discuss
what entropic analyses tell us about the difference. This has applications to
quantum cryptography, where it can be crucial to eliminate the possibility of
classical causes. We discuss the achievements and limitations of the entropic
approach in comparison to other techniques and point out the main open
problems.Comment: 19 (+3) pages, 5 (+1) figures. A few minor updates and corrections.
There is a small error in the published version of this manuscript: the claim
in the last sentence of Section 2(a)(ii) should be restricted to four
variables. This is correct in the arXiv versio
Measuring processes and the Heisenberg picture
In this paper, we attempt to establish quantum measurement theory in the
Heisenberg picture. First, we review foundations of quantum measurement theory,
that is usually based on the Schr\"{o}dinger picture. The concept of instrument
is introduced there. Next, we define the concept of system of measurement
correlations and that of measuring process. The former is the exact counterpart
of instrument in the (generalized) Heisenberg picture. In quantum mechanical
systems, we then show a one-to-one correspondence between systems of
measurement correlations and measuring processes up to complete equivalence.
This is nothing but a unitary dilation theorem of systems of measurement
correlations. Furthermore, from the viewpoint of the statistical approach to
quantum measurement theory, we focus on the extendability of instruments to
systems of measurement correlations. It is shown that all completely positive
(CP) instruments are extended into systems of measurement correlations. Lastly,
we study the approximate realizability of CP instruments by measuring processes
within arbitrarily given error limits.Comment: v
Operator theory and function theory in Drury-Arveson space and its quotients
The Drury-Arveson space , also known as symmetric Fock space or the
-shift space, is a Hilbert function space that has a natural -tuple of
operators acting on it, which gives it the structure of a Hilbert module. This
survey aims to introduce the Drury-Arveson space, to give a panoramic view of
the main operator theoretic and function theoretic aspects of this space, and
to describe the universal role that it plays in multivariable operator theory
and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page