# Roope Uola

PhD studentRoom: B-106

Phone: +49 271 740 3774

## Preprints

See also arxiv

Roope Uola, Tristan Kraft, Jiangwei Shang, Xiao-Dong Yu and Otfried Gühne
*
Quantifying quantum resources with conic programming
*

arXiv:1812.09216

Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g. joint measurability, POVMs simulable by projective measurements, and state assemblages preparable with a given Schmidt number.

Roope Uola, Giuseppe Vitagliano and Costantino Budroni
*
Leggett-Garg macrorealism and the quantum nondisturbance conditions
*

arXiv:1812.02346

We investigate the relation between a refined version of Leggett and Garg conditions for macrorealism, namely the no-signaling-in-time (NSIT) conditions, and the quantum mechanical notion of nondisturbance, and obtain a compatibility relation among an arbitrary number of observables based on their minimally disturbing sequential implementation. We show that all NSIT conditions are satisfied for any state preparation if and only if simple compatibility criteria on the state-update rules relative to the observables, i.e. quantum instruments, are met. Motivated by this connection, we prove some structural results on nondisturbance of two or more observables, such as the existence of noncommuting and two-way nondisturbing observables, and pairwise but not triplewise nondisturbing observables. Moreover, we discuss perspectives for a resource theory of quantum disturbance based on the notion of macrorealism by defining a general measure of disturbance and investigating which operations do not increase it.

## Publications

Ana C. S. Costa, Roope Uola and Otfried Gühne
*
Entropic Steering Criteria: Applications to Bipartite and Tripartite
Systems
*

Entropy *20*,
763
(2018),
arXiv:1808.01198

The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and (iii) joint convexity of a corresponding relative entropy. Our study extends the former analysis to Tsallis and R\'enyi entropies on bipartite and tripartite systems. As examples, we investigate the steerability of the three-qubit GHZ and W states.

Ana C. S. Costa, Roope Uola and Otfried Gühne
*
Steering criteria from general entropic uncertainty relations
*

Phys. Rev. A *98*,
050104
(2018),
arXiv:1710.04541

The effect of steering describes a possible action at a distance via measurements but characterizing the quantum states that can be used for this task remains difficult. We provide a method to derive sufficient criteria for steering from entropic uncertainty relations using generalized entropies. We demonstrate that the resulting criteria outperform existing criteria in several scenarios; moreover, they allow one to detect weakly steerable states.

Roope Uola, Fabiano Lever, Otfried Gühne and Juha-Pekka Pellonpää
*
Unified picture for spatial, temporal and channel steering
*

Phys. Rev. A *97*,
032301
(2018),
arXiv:1707.09237

Quantum steering describes how local actions on a quantum system can affect another, space-like separated, quantum state. Lately, quantum steering has been formulated also for time-like scenarios and for quantum channels. We approach all the three scenarios as one using tools from Stinespring dilations of quantum channels. By applying our technique we link all three steering problems one-to-one with the incompatibility of quantum measurements, a result formerly known only for spatial steering. We exploit this connection by showing how measurement uncertainty relations can be used as tight steering inequalities for all three scenarios. Moreover, we show that certain notions of temporal and spatial steering are fully equivalent and prove a hierarchy between temporal steering and macrorealistic hidden variable models.

Jukka Kiukas, Costantino Budroni, Roope Uola and Juha-Pekka Pellonpää
*
Continuous variable steering and incompatibility via state-channel
duality
*

Phys. Rev. A *96*,
042331
(2017),
arXiv:1704.05734

The term Einstein-Podolsky-Rosen steering refers to a quantum correlation intermediate between entanglement and Bell nonlocality, which has been connected to another fundamental quantum property: measurement incompatibility. In the finite-dimensional case, efficient computational methods to quantify steerability have been developed. In the infinite-dimensional case, however, less theoretical tools are available. Here, we approach the problem of steerability in the continuous variable case via a notion of state-channel correspondence, which generalizes the well-known Choi-Jamio\l{}kowski correspondence. Via our approach we are able to generalize the connection between steering and incompatibility to the continuous variable case and to connect the steerability of a state with the incompatibility breaking property of a quantum channel, e.g., noisy NOON states and amplitude damping channels. Moreover, we apply our methods to the Gaussian steering setting, proving, among other things, that canonical quadratures are sufficient for steering Gaussian states.

Roope Uola, Kimmo Luoma, Tobias Moroder and Teiko Heinosaari
*
Adaptive strategy for joint measurements
*

Phys. Rev. A *94*,
022109
(2016),
arXiv:1604.08724

We develop a technique to find simultaneous measurements for noisy quantum observables in finite-dimensional Hilbert spaces. We use the method to derive lower bounds for the noise needed to make incompatible measurements jointly measurable. Using our strategy together with recent devel- opments in the field of one-sided quantum information processing we show that the attained lower bounds are tight for various symmetric sets of quantum measurements. We use this characterisation to prove the existence of so called 4-Specker sets in the qubit case.

Tobias Moroder, Oleg Gittsovich, Marcus Huber, Roope Uola and Otfried Gühne
*
Steering maps and their application to dimension-bounded steering
*

Phys. Rev. Lett. *116*,
090403
(2016),
arXiv:1412.2623

The existence of quantum correlations that allow one party to steer the quantum state of another party is a counterintuitive quantum effect that has been described already at the beginning of the past century. Steering occurs if entanglement can be proven although the description of the measurements on one party is not known, while the other side is characterized. We introduce the concept of steering maps that allow to unlock the sophisticated techniques developed in regular entanglement detection to be used for certifying steerability. As an application we show that this allows to go even beyond the canonical steering scenario, enabling a generalized dimension-bounded steering where one only assumes the Hilbert space dimension on the characterized side, but no description of the measurements. Surprisingly this does not weaken the detection strength of very symmetric scenarios that have recently been carried out in experiments.

Roope Uola, Costantino Budroni, Otfried Gühne and Juha-Pekka Pellonpää
*
One-to-one mapping between steering and joint measurability problems
*

Phys. Rev. Lett. *115*,
230402
(2015),
arXiv:1507.08633

Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it has been recently proven that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice's observables. We show that such an equivalence holds in general, namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.

Erkka Haapasalo, Juha-Pekka Pellonpää and Roope Uola
*
Compatibility properties of extreme quantum observables
*

Lett. Math. Phys. *105*,
661-673
(2015),
arXiv:1404.4172

Recently a problem concerning the equivalence of joint measurability and coexistence of quantum observables was solved [15]. In this paper we generalize two known joint measurability results from sharp observables to the class of extreme observables and study relationships between coexistence, joint measurability, and post-processing of quantum observables when an extreme observable is involved. We also discuss another notion of compatibility and provide a counterexample separating this from the former notions.

Roope Uola, Tobias Moroder and Otfried Gühne
*
Joint measurability of generalized measurements implies classicality
*

Phys. Rev. Lett. *113*,
160403
(2014),
arXiv:1407.2224

The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.