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An invitation to quantum incompatibility
The purpose of this paper is to give a concise overview of some of the central aspects of incompatibility, as a common ground for several famous impossibility statements within quantum theory.
Incompatibility of quantum channels
A characterization of the compatibility relation in terms of concatenation and conjugation is derived and it is shown that all pairs of sufficiently noisy quantum channels are compatible.
Stability of quantum states of finite macroscopic systems against classical noises, perturbations from environments, and local measurements.
The mechanism of symmetry-breaking in finite systems of finite volume V is discussed and it is shown that if a state, pure or mixed, has the "cluster property," then it is stable against local measurements, and vice versa.
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…
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…
On Halting Process of Quantum Turing Machine
We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, cannot avoid the notion of…
Dynamical aspects of quantum entanglement for weakly coupled kicked tops.
- H. Fujisaki, T. Miyadera, A. Tanaka
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 19 November 2002
It is shown that the increment in the strength of chaos does not enhance the production rate of entanglement when the coupling is weak enough and the subsystems (kicked tops) are strongly chaotic.
RELATION BETWEEN INFORMATION AND DISTURBANCE IN QUANTUM KEY DISTRIBUTION PROTOCOL WITH CLASSICAL ALICE
- T. Miyadera
- Computer Science
- 12 May 2011
The "semiquantum" key distribution protocol introduced by Zou et al. is examined and a trade-off inequality between information gained by Eve and the disturbance observed by legitimate users is derived.
Approximating relational observables by absolute quantities: a quantum accuracy-size trade-off
The notion that any physical quantity is defined and measured relative to a reference frame is traditionally not explicitly reflected in the theoretical description of physical experiments where,…
Strongly Incompatible Quantum Devices
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint…