# Quantum Limits of Measurements and Uncertainty Principle

@article{Ozawa2015QuantumLO, title={Quantum Limits of Measurements and Uncertainty Principle}, author={Masanao Ozawa}, journal={arXiv: Quantum Physics}, year={2015} }

In this paper, we show how the Robertson uncertainty relation gives certain intrinsic quantum limits of measurements in the most general and rigorous mathematical treatment. A general lower bound for the product of the root-mean-square measurement errors arising in joint measurements of noncommuting observables is established. We give a rigorous condition for holding of the standard quantum limit (SQL) for repeated measurements, and prove that if a measuring instrument has no larger root-mean…

## 21 Citations

### Uncertainty relations for generalized quantum measurements and completely positive maps

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- 2003

The Heisenberg uncertainty relation for measurement noise and disturbance states that any position measurement with noise /spl epsiv/ brings the momentum disturbance not less than h/2/spl epsiv/.…

### Soundness and completeness of quantum root-mean-square errors

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In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible…

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In the present article, we discuss two types of uncertainty relations in Quantum Mechanics–multiplicative and additive inequalities for two canonical observables. The multiplicative uncertainty…

### Universally valid uncertainty relations in general quantum systems

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We study universally valid uncertainty relations in general quantum systems described by general $\sigma$-finite von Neumann algebras to foster developing quantitative analysis in quantum systems…

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This paper quantifies precisely Heisenberg’s intuition on the disturbance of an observable induced by the approximate measurement of another one and derives a stronger error-disturbance relation for this scenario.

### Quantum measurement and uncertainty relations in photon polarization

- Physics
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Recent theoretical and experimental studies have given raise to new aspects in quantum measurements and error-disturbance uncertainty relations. After a brief review of these issues, we present an…

### Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation

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An experimental test of Ozawa's relation for a single-photon polarization qubit is reported, exploiting a more general class of quantum measurements than the class of projective measurements.

### Heisenberg's original derivation of the uncertainty principle and its universally valid reformulations

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Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be…

### Quantum Measurements and State Reduction

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In quantum mechanics, the state reduction due to a measurement is called the collapse of a wavefunction. Its study is often perceived as a somewhat mystical phenomenon because of the lack of proper…

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