Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1201.6628 · Physica Scripta

How can we check the uncertainty relation?

Vladimir N. Chernega

Published Feb 1, 2012• 7 citations
arXivHTMLPDF

Abstract

The state-extended uncertainty relations generalizing the Robertson–Schrödinger inequality are presented in a form appropriate for an experimental check by homodyne photon-state detection. The method of qubit portrait of qudit states identified with the tomographic probability distributions is discussed in order to analyze the entanglement of the two-mode field.

DOI
10.1088/0031-8949/2012/t147/014006

Related papers

Two-mode optical tomograms: a possible experimental check of the Robertson uncertainty relations

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +1 more

The experimental check of two--mode Robertson uncertainty relations and inequalities for highest quadrature moments is suggested by using homodyne photon detection. The relation between optical tomograms and symplectic tomograms is used to connect the tomographic dispersion matrix and the quadrature components dispersion matrix of the two--mode field states.

arXiv:1202.0434•Physica Scripta•Feb 1, 2012•5 citations

A possible experimental check of the uncertainty relations by means of homodyne measuring photon quadrature

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +1 more

We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schrödinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states.

arXiv:0811.4115•Nov 25, 2008•4 citations

A Possible Experimental Check of the Uncertainty Relations by Means of Homodyne Measuring Field Quadrature

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +1 more

We suggest to use the photon homodyne detection experimental data for checking the Heisenberg and Schroedinger-Robertson uncertainty relations, by means of measuring optical tomograms of the photon quantum states. Examples of Gaussian states are discussed.

Advanced Science Letters•Dec 1, 2009•28 citations

States in the Weyl–Wigner and tomographic-probability representations and entropic inequalities

Margarita A. Man’ko, Vladimir I. Man’ko

The homodyne tomographic description of photon states is applied to obtain the evolution equation for the system state in both the quantum and classical domains. Entropic inequalities for optical tomograms and the bounds in uncertainty relations are discussed in the context of a possible experimental check in quantum optics using homodyne photon detection and microwave detection.

Physica Scripta•Feb 1, 2012•7 citations

Robertson–Schrödinger uncertainty relation for qubits: a visual approach

Julio C. Gutiérrez-Vega

Abstract The uncertainty principle sets a limit to our capacity to predict the outcomes of two incompatible measurements. The Heisenberg uncertainty relation for two arbitrary observables A and B is usually discussed in textbooks. However, little or no attention is paid to the fact that Schrödinger generalised the Heisenberg relation taking into account the covariance between the observables A and B . This extended inequality is known as the Robertson–Schrödinger uncertainty relation. Here, we demonstrate the less known fact that two-level quantum states, i.e., qubits, satisfy the equality of the Robertson–Schrödinger uncertainty relation for two arbitrary observables A and B . Taking advantage of the homomorphism between SU(2) and SO(3) groups, it is possible to map the distributions of the expectation values and variances of the observables, and the Heisenberg and covariance terms on the Bloch sphere. The graphical visualisation of the relevant quantities involved in the uncertainty relations allows us to distinguish specific properties and symmetries that are not so evident in the algebraic formalism.

European Journal of Physics•Jan 8, 2021•4 citations

Qubit-portraits of qudit states and quantum correlations

Cosmo Lupo, V. I. Man’ko, Giuseppe Marmo

The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.

•Nov 21, 2012•23 citations
The state-extended uncertainty relations generalizing the Robertson–Schrödinger inequality are presented in a form appropriate for an experimental check by homodyne photon-state detection. The method of qubit portrait of qudit states identified with the tomographic probability distributions is discussed in order to analyze the entanglement of the two-mode field.
Abstract The uncertainty principle sets a limit to our capacity to predict the outcomes of two incompatible measurements. The Heisenberg uncertainty relation for two arbitrary observables A and B is usually discussed in textbooks. However, little or no attention is paid to the fact that Schrödinger generalised the Heisenberg relation taking into account the covariance between the observables A and B . This extended inequality is known as the Robertson–Schrödinger uncertainty relation. Here, we demonstrate the less known fact that two-level quantum states, i.e., qubits, satisfy the equality of the Robertson–Schrödinger uncertainty relation for two arbitrary observables A and B . Taking advantage of the homomorphism between SU(2) and SO(3) groups, it is possible to map the distributions of the expectation values and variances of the observables, and the Heisenberg and covariance terms on the Bloch sphere. The graphical visualisation of the relevant quantities involved in the uncertainty relations allows us to distinguish specific properties and symmetries that are not so evident in the algebraic formalism.
The machinery of qubit-portraits of qudit states, recently presented, is consider here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated to a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples, we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot in the case of qutrit Werner states.