416 research outputs found
Generalized Landau-Pollak Uncertainty Relation
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 positive operator valued
measures. A nontrivial but slightly weak inequality that can treat an arbitrary
number of positive operator valued measures is also presented.Comment: Simplified the proofs. To be published in Phys.Rev.
Wigner-Araki-Yanase theorem on Distinguishability
The presence of an additive conserved quantity imposes a limitation on the
measurement process. According to the Wigner-Araki-Yanase theorem, the perfect
repeatability and the distinguishability on the apparatus cannot be attained
simultaneously. Instead of the repeatability, in this paper, the
distinguishability on both systems is examined. We derive a trade-off
inequality between the distinguishability of the final states on the system and
the one on the apparatus. The inequality shows that the perfect
distinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.
No-Cloning Theorem on Quantum Logics
This paper discusses the no-cloning theorem in a logico-algebraic approach.
In this approach, an orthoalgebra is considered as a general structure for
propositions in a physical theory. We proved that an orthoalgebra admits
cloning operation if and only if it is a Boolean algebra. That is, only
classical theory admits the cloning of states. If unsharp propositions are to
be included in the theory, then a notion of effect algebra is considered. We
proved that an atomic Archimedean effect algebra admitting cloning operation is
a Boolean algebra. This paper also presents a partial result indicating a
relation between cloning on effect algebras and hidden variables.Comment: To appear in J. Math. Phy
Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
A limitation on simultaneous measurement of two arbitrary positive operator
valued measures is discussed. In general, simultaneous measurement of two
noncommutative observables is only approximately possible. Following Werner's
formulation, we introduce a distance between observables to quantify an
accuracy of measurement. We derive an inequality that relates the achievable
accuracy with noncommutativity between two observables. As a byproduct a
necessary condition for two positive operator valued measures to be
simultaneously measurable is obtained.Comment: 7 pages, 1 figure. To appear in Phys. Rev.
Information-Disturbance Theorem for Mutually Unbiased Observables
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
Quantum Kolmogorov Complexity and Quantum Key Distribution
We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol
in the light of quantum algorithmic information. While Shannon's information
theory needs a probability to define a notion of information, algorithmic
information theory does not need it and can assign a notion of information to
an individual object. The program length necessary to describe an object,
Kolmogorov complexity, plays the most fundamental role in the theory. In the
context of algorithmic information theory, we formulate a security criterion
for the quantum key distribution by using the quantum Kolmogorov complexity
that was recently defined by Vit\'anyi. We show that a simple BB84 protocol
indeed distribute a binary sequence between Alice and Bob that looks almost
random for Eve with a probability exponentially close to 1.Comment: typos correcte
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