The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of… (More)
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)
It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it… (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)
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative… (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)