Martin Plávala

Postdoc
Room: B-005
Phone:
martin.plavala@uni-siegen.dePreprints
See also arxiv
Mark Girard, Martin Plávala and Jamie Sikora
Jordan products of quantum channels and their compatibility
arXiv:2009.03279
Given two quantum channels, we examine the task of determining whether they
are compatible - meaning that one can perform both channels simultaneously but,
in the future, choose exactly one channel whose output is desired (while
forfeiting the output of the other channel). We show several results concerning
this task. First, we show it is equivalent to the quantum state marginal
problem, i.e., every quantum state marginal problem can be recast as the
compatibility of two channels, and vice versa. Second, we show that compatible
measure-and-prepare channels (i.e., entanglement-breaking channels) do not
necessarily have a measure-and-prepare compatibilizing channel. Third, we
extend the notion of the Jordan product of matrices to quantum channels and
present sufficient conditions for channel compatibility. These Jordan products
and their generalizations might be of independent interest. Last, we formulate
the different notions of compatibility as semidefinite programs and numerically
test when families of partially dephasing-depolaring channels are compatible.
Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos and Martin Plavala
Entangleability of cones
arXiv:1911.09663
We solve a long-standing conjecture by Barker, proving that the minimal and
maximal tensor products of two finite-dimensional proper cones coincide if and
only if one of the two cones is generated by a linearly independent set. Here,
given two proper cones $C_1$, $C_2$, their minimal tensor product is the cone
generated by products of the form $x_1 \otimes x_2$, where $x_1 \in C_1$ and
$x_2 \in C_2$, while their maximal tensor product is the set of tensors that
are positive under all product functionals $f_1 \otimes f_2$, where $f_1$ is
positive on $C_1$ and $f_2$ is positive on $C_2$. Our proof techniques involve
a mix of convex geometry, elementary algebraic topology, and computations
inspired by quantum information theory. Our motivation comes from the
foundations of physics: as an application, we show that any two non-classical
systems modelled by general probabilistic theories can be entangled.
Martin Plávala and Mário Ziman
Popescu-Rohrlich box implementation in general probabilistic theory of
processes
arXiv:1708.07425
It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound
for Bell inequality) do exist in the existing structures of both quantum and
classical theory. In particular, we design an explicit example of
measure-and-prepare nonlocal (but no-signaling) channel being the realization
of nonlocal and no-signaling Popescu-Rohrlich box within the generalized
probabilistic theory of processes. Further we present a post-selection-based
spatially non-local implementation and show it does not require truly quantum
resources, hence, improving the previously known results. Interpretation and
potential (spatially non-local) simulation of this form of process nonlocality
and the protocol is discussed.
Publications
Anna Jenčová and Martin Plávala
Structure of quantum and classical implementations of Popescu-Rohrlich
box
Phys. Rev. A 10,
, 042208
(2020),
arXiv:1907.08933
We construct implementations of the PR-box using quantum and classical
channels as state spaces. In both cases our constructions are very similar and
they share the same idea taken from general probabilistic theories and the
square state space model. We construct all quantum qubit channels that
maximally violate a given CHSH inequality, we show that they all are
entanglement-breaking channels, that they have certain block-diagonal structure
and we present some examples of such channels.
Anna Jenčová and Martin Plávala
On the properties of spectral effect algebras
Quantum 3,
148
(2019),
arXiv:1811.12407
The aim of this paper is to show that there can be either only one or
uncountably many contexts in any spectral effect algebra, answering a question
posed in [S. Gudder, Convex and Sequential Effect Algebras, (2018),
arXiv:1802.01265]. We also provide some results on the structure of spectral
effect algebras and their state spaces and investigate the direct products and
direct convex sums of spectral effect algebras. In the case of spectral effect
algebras with sharply determining state space, stronger properties can be
proved: the spectral decompositions are essentially unique, the algebra is
sharply dominating and the set of its sharp elements is an orthomodular
lattice. The article also contains a list of open questions that might provide
interesting future research directions.
Teiko Heinosaari, Leevi Leppäjärvi and Martin Plávala
No-free-information principle in general probabilistic theories
Quantum 3,
157
(2019),
arXiv:1808.07376
In quantum theory, the no-information-without-disturbance and
no-free-information theorems express that those observables that do not disturb
the measurement of another observable and those that can be measured jointly
with any other observable must be trivial, i.e., coin tossing observables. We
show that in the framework of general probabilistic theories these statements
do not hold in general and continue to completely specify these two classes of
observables. In this way, we obtain characterizations of the probabilistic
theories where these statements hold. As a particular class of state spaces we
consider the polygon state spaces, in which we demonstrate our results and show
that while the no-information-without-disturbance principle always holds, the
validity of the no-free-information principle depends on the parity of the
number of vertices of the polygons.
Martin Plávala
Conditions for the compatibility of channels in general probabilistic
theory and their connection to steering and Bell nonlocality
Phys. Rev. A 96,
052127
(2017),
arXiv:1707.08650
We derive general conditions for the compatibility of channels in general
probabilistic theory. We introduce formalism that allows us to easily formulate
steering by channels and Bell nonlocality of channels as generalizations of the
well-known concepts of steering by measurements and Bell nonlocality of
measurements. The generalization does not follow the standard line of thinking
stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and
Bell nonlocality as entanglement-assisted incompatibility tests. We show that
all of the proposed definitions are, in the special case of measurements, the
same as the standard definitions, but not all of the known results for
measurements generalize to channels. For example, we show that for quantum
channels, steering is not a necessary condition for Bell nonlocality. We
further investigate the introduced conditions and concepts in the special case
of quantum theory and we provide many examples to demonstrate these concepts
and their implications.
Anna Jenčová and Martin Plávala
Conditions on the existence of maximally incompatible two-outcome
measurements in General Probabilistic Theory
Phys. Rev. A 96,
022113
(2017),
arXiv:1703.09447
We formulate the necessary and sufficient conditions for the existence of a
pair of maximally incompatible two-outcome measurements in a finite dimensional
General Probabilistic Theory. The conditions are on the geometry of the state
space, they require existence of two pairs of parallel exposed faces with
additional condition on their intersections. We introduce the notion of
discrimination measurement and show that the conditions for a pair of
two-outcome measurements to be maximally incompatible are equivalent to
requiring that a (potential, yet non-existing) joint measurement of the
maximally incompatible measurements would have to discriminate affinely
dependent points. We present several examples to demonstrate our results.
Martin Plávala
All measurements in a probabilistic theory are compatible if and only if
the state space is a simplex
Phys. Rev. A 94,
042108
(2016),
arXiv:1608.05614
We study the compatibility of measurements on finite-dimensional compact
convex state space in the framework of general probabilistic theory. Our main
emphasis is on formulation of necessary and sufficient conditions for
two-outcome measurements to be compatible and we use these conditions to show
that there exist incompatible measurements whenever the state space is not a
simplex. We also formulate the linear programming problem for the compatibility
of two-outcome measurements.
Anna Jenčová and Martin Plávala
Conditions for optimal input states for discrimination of quantum
channels
J. Math. Phys. 57,
, 122203
(2016),
arXiv:1603.01437
We find optimality conditions for testers in discrimination of quantum
channels. These conditions are obtained using semidefinite programming and are
similar to optimality conditions for POVMs obtained by Holevo for ensembles of
quantum states. We get a simple condition for existence of an optimal tester
with any given input state with maximal Schmidt rank, in particular with a
maximally entangled input state and we show the pitfalls of using input states
with not maximal Schmidt rank. In case when maximally entangled state is not
the optimal input state an error estimate is obtained. The results for
maximally entangled input state are applied to covariant channels, qubit
channels, unitary channels and simple projective measurements.