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We derive a novel version of information-disturbance theorems for mutually unbiased observables. We show that the information gain by Eve inevitably makes the outcomes by Bob in the conjugate basis not only erroneous but random.

It has been shown that Information-Disturbance theorem can play an important role in security proof of quantum cryptography. The theorem is by itself interesting since it can be regarded as an information theo-retic version of uncertainty principle. It, however, has been able to treat restricted situations. In this paper, the restriction on the source is… (More)

People make logically inconsistent probability judgments. The " Linda " problem is a well-known example, which often elicits a conjunction/disjunction fallacy: probability of constituent event A (B) judged more/less likely than their con-junction/disjunction. The Quantum Judgment model (QJM, Busemeyer et al 2011) explains such errors, which are not… (More)

General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination problems in general probabilistic theories using a Bayesian strategy. After re-formulation of the theories with… (More)

On one-dimensional two-way infinite quantum lattice system, a property of translation-ally invariant stationary states with nonvanishing current expectation is investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show that spectrum of the unitary operators ,… (More)

An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives,… (More)

- So Strange, “Weak Values, Dmitri Sokolovski, Maria Diaz, Haroko Kalea, Paul Busch +1 other
- 2016

Suppose we make a series of measurements on a chosen quantum system. The outcomes of the measurements form a sequence of random events, which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network connecting all possible outcomes. The paths are shaped from the virtual paths of the… (More)

- Claudio Carmeli, Teiko Heinosaari, Daniel Reitzner, Jussi Schultz, Alessandro Toigo, Takayuki Miyadera
- 2016

We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy separately. We introduce the index of incompatibility as a quantifier of incompatibility in this multi-copy setting, as well as… (More)