Teiko Heinosaari

Performing a quantum measurement yields two different results: a classical outcome drawn from a probability distribution, according to Born’s rule, and a quantum outcome corresponding to the post-measurement state. Quantum devices that provide both outcomes can be described through quantum instruments. In a realistic scenario, one can expect that the observer’s obtained classical and quantum outcomes are non-ideal: this can be due to experimental limitations, but could also be explained by adversarial interference, that is, a second party that disturbs the device through a concealed measurement to obtain information. The second scenario can be interpreted through quantum compatibility, as it implies that both the observer’s instrument and the adversary’s measurement can be performed simultaneously. In this work, we show how the noise of the observer’s device relates to the amount of information that the adversary can obtain. We study scenarios in which the adversary aims to acquire information on the same basis as the observer’s measurement, or on a mutually unbiased basis with respect to the observer’s basis. In both cases, we derive necessary and sufficient conditions for the compatibility of a single qubit non-ideal quantum instrument and a noisy meter, from which we obtain the maximum amount of information that the adversary can extract in terms of the noise parameters of the observer’s instrument. Finally, we provide the device implementation from the adversary’s point of view for the same basis scenario.

Useful applications of quantum information technologies can be found by identifying tasks in which quantum resources outperform their classical counterparts. In this work, we introduce a two-party communication primitive, random exclusion code (REC), which is a single-shot prepare-and-measure protocol where a sender encodes a random message into a shorter sequence and a receiver attempts to a randomly chosen letter in the original message. We present quantum advantages in RECs in two ways: and . We show that RECs with quantum resources achieve higher success probabilities than classical strategies. We verify that, with the additional constraint that successful outcomes occur uniformly and without error, the quantum resources required to describe detection events of RECs have a smaller dimension than classical ones. We also show that a guessing counterpart, random access codes, may not have a dimension advantage over classical resources. Our results elucidate various possibilities of achieving quantum advantages in two-party communication.

Quantum guessing games offer a structured approach to analyzing quantum information processing, where information is encoded in quantum states and extracted through measurement. An additional aspect of this framework is the influence of partial knowledge about the input on the optimal measurement strategies. This kind of side information can significantly influence the guessing strategy and earlier work has shown that the timing of such side information, whether revealed before or after the measurement, can affect the success probabilities. In this work, we go beyond this established distinction by introducing the concept of metainformation. Metainformation is information about information, and in our context it is knowledge that additional side information of certain type will become later available, even if it is not yet provided. We show that this seemingly subtle difference between having no expectation of further information versus knowing it will arrive can have operational consequences for the guessing task. Our results demonstrate that metainformation can, in certain scenarios, enhance the achievable success probability up to the point that post-measurement side information becomes as useful as prior-measurement side information, while in others it offers no benefit. By formally distinguishing metainformation from actual side information, we uncover a finer structure in the interplay between timing, information, and strategy, offering new insights into the capabilities of quantum systems in information processing tasks.

Simultaneously implementing two arbitrary quantum measurements on the same system is impossible. The consequence of this limitation is that selecting one measurement actively excludes other possibilities. Two incompatible choices can then be forced together only at the cost of adding enough noise to the measurements. An intriguing alternative is to postpone the choice, or part of it, until a later stage. We explore the advantages of this deferred decision-making and discover that the benefits critically depend on the assumptions about the forthcoming choice. In certain scenarios postponing the choice introduces no additional cost, while in others partial postponement can be effectively the same as full postponement.

We investigate finite effect algebras and their classification. We show that an effect algebra with n elements has at least n − 2 and at most ( n − 1 ) ( n − 2 ) / 2 nontrivial defined sums. We characterize finite effect algebras with these minimal and maximal number of defined sums. The latter effect algebras are scale effect algebras (i.e. subalgebras of [0,1]), and only those. We prove that there is exactly one scale effect algebra with n elements for every integer n ⩾ 2 . We show that a finite effect algebra is quantum effect algebra (i.e. a subeffect algebra of the standard quantum effect algebra) if and only if it has a finite set of order-determining states. Among effect algebras with 2–6 elements, we identify all quantum effect algebras.

A prepare-and-measure scenario is naturally described by a communication matrix that collects all conditional outcome probabilities of the scenario into a row-stochastic matrix. The set of all possible communication matrices is partially ordered via the possibility to transform one matrix to another by pre- and post-processings. By considering maximal elements in this preorder for a subset of matrices implementable in a given theory, it becomes possible to identify communication matrices of maximum utility, i.e., matrices that are not majorized by any other matrices in the theory. The identity matrix of an appropriate size is the greatest element in classical theories, while the maximal elements in quantum theory have remained unknown. We completely characterize the maximal elements in quantum theory, thereby revealing the essential structure of the set of quantum communication matrices. In particular, we show that the identity matrix is the only maximal element in quantum theory but, as opposed to a classical theory, it is not the greatest element. Quantum theory can hence be seen to be distinct from classical theory by the existence of incompatible communication matrices.

Quantum computing is a highly abstract scientific discipline, which, however, is expected to have great practical relevance in future information technology. This forces educators to seek new methods to teach quantum computing for students with diverse backgrounds and with no prior knowledge of quantum physics. We have developed an online course built around an interactive quantum circuit simulator designed to enable easy creation and maintenance of course material with ranging difficulty. The immediate feedback and automatically evaluated tasks lower the entry barrier to quantum computing for all students, regardless of their background.

The emergence of quantum computing proposes a revolutionary paradigm that can radically transform numerous scientific and industrial application domains. However, realizing this promise in industrial applications is far from being practical today. In this paper, we discuss industry experiences with respect to quantum computing, and the gap between quantum software engineering research and state-of-the-practice in industry-scale quantum computing.

Quantumness refers to the peculiar and counterintuitive characteristics exhibited by quantum systems. Tsirelson inequalities have emerged as a powerful tool in quantum theory to detect quantumness and entanglement of harmonic oscillators, spins undergoing uniform precession, and anharmonic systems. In this paper we harness the versatility of Tsirelson inequalities to address two distinct problems: detecting cheating in classic shell games and probing quantumness in spatially separated systems and harmonic oscillators. By adopting a black-box approach and a geometric characterization of the space of conditional probabilities, we demonstrate that Tsirelson inequalities can be used in both scenarios, enabling us to uncover quantum signatures and identify cheaters in a single unified framework. This connection provides an intuitive different perspective on quantumness of mechanical systems.

Encoding and decoding are the two key steps in information processing. In this work, we study the encoding and decoding capabilities of operational theories in the context of information-storability game, where the task is to freely choose a set of states from which one state is chosen at random and by measuring the state it must be identified; a correct guess results in as many utiles as the number of states in the chosen set and an incorrect guess means a penalty of a fixed number of utiles. We connect the optimal winning strategy of the game to the amount of information that can be stored in a given theory, called the information storability of the theory, and show that one must use so-called nondegradable sets of states and nondegradable measurements whose encoding and decoding properties cannot be reduced. We demonstrate that there are theories where the perfect discrimination strategy is not the optimal one so that the introduced game can be used as an operational test for super information storability. We further develop the concept of information storability by giving new useful conditions for calculating it in specific theories.