Related papers: Causal State Estimation and the Heisenberg Uncerta…
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.…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
From the noncommutative nature of quantum mechanics, estimation of canonical observables $\hat{q}$ and $\hat{p}$ is essentially restricted in its performance by the Heisenberg uncertainty relation, $\mean{\Delta \hat{q}^2}\mean{\Delta…
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…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
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.…
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of…
Heisenberg's uncertainty relation for measurement noise and disturbance states that any position measurement with noise epsilon brings the momentum disturbance not less than hbar/2epsilon. This relation holds only for restricted class of…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
As a key method in dealing with uncertainties, feedback has been understood fairly well in classical control theory. But for quantum control systems, the capability of measurement-based feedback control (MFC) has not been investigated…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
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…
Finding optimal and noise robust probe states is a key problem in quantum metrology. In this paper we propose Markov dynamics as a possible mechanism for generating such states, and show how the Heisenberg scaling emerges for systems with…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
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…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders.…