Related papers: How can we check the uncertainty relation?
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
Necessary and sufficient conditions for the nonclassicality of bosonic quantum states are formulated by introducing nonclassicality filters and nonclassicality quasiprobability distributions. Regular quasiprobabilities are constructed from…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of…
A self-homodyne detection scheme is proposed to perform two-mode tomography on a twin-beam state at the output of a nondegenerate optical parametric amplifier. This scheme has been devised to improve the matching between the local…
Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous variable entanglement. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one…
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the…
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertatinty relation, as well as a couple of…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
We experimentally test invariance properties of the six-photonic-qubits generalization of a singlet state. Our results clearly corroborate with theory. The invariance properties are useful to beat some types of decoherence. We also…
Quantum physics constrains the accuracy of joint measurements of incompatible observables. Here we test tight measurement-uncertainty relations using single photons. We implement two independent, idealized uncertainty-estimation methods,…
A smooth function of the second moments of $N$ continuous variables gives rise to an uncertainty relation if it is bounded from below. We present a method to systematically derive such bounds by generalizing an approach applied previously…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental…
The phenomenon of quantum steering and probabilistic meaning of the correlations are discussed for the state of the single qudit. The method of qubit portrait of the qudit states is used to extend the known steering detection inequality to…
The full characterization of quantum states of light is a central task in quantum optics and information science. Double homodyne detection provides a powerful method for the direct measurement of the Husimi Q quasi-probability…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…
We examine two conditions that can be used to detect bipartite entanglement, and show that they can be used to provide lower bounds on the negativity of states. We begin with two-qubit states, and then show how what was done there can be…