Related papers: The Uncertainty Relation for Smooth Entropies
Suppose one wants to certify that a quantum channel is not entanglement-breaking. I consider all four combinations of trusted and untrusted devices at the input and output of the channel, finding that the most interesting is a trusted…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
Uncertainty principle has a fundamental role in quantum theory. This principle states that it is not possible to measure two incompatible observers simultaneously. The uncertainty principle is expressed logically in terms of standard…
We present a family of entropic uncertainty relations for pointer-based simultaneous measurements of conjugate observables. The lower bounds of these relations explicitly incorporate the influence of the measurement apparatus. We achieve…
We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations…
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…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
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 relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…
The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from…