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The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated…
It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
Adaptive techniques make practical many quantum measurements that would otherwise be beyond current laboratory capabilities. For example: they allow discrimination of nonorthogonal states with a probability of error equal to the Helstrom…
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high…
Measurement-induced back action, a direct consequence of the Heisenberg Uncertainty Principle, is the defining feature of quantum measurements. We use quantum measurement theory to analyze the recent experiment of Safavi-Naeini et al.…
In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…
State-of-the-art sensors of force, motion and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached…
Heisenberg's uncertainty principle has been understood to set a limitation on measurements; however, the long-standing mathematical formulation established by Heisenberg, Kennard, and Robertson does not allow such an interpretation.…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality…
A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift…
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
The uncertainty principle generally prohibits determination of certain pairs of quantum mechanical observables with arbitrary precision and forms the basis of indeterminacy in quantum mechanics. It was Heisenberg who used the famous…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…