2012/05/23 by J. Solomon Ivan, J Solomon Ivan, Ivan, J Solomon +6
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1205.5132
35 pages
arxiv created 2012/05/23 · openalex publication_date 2012/05/23 · arxiv updated 2012/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general quantum state. Particular emphasis is given to the action of unitary symmetry operations of the system on the chosen observables, and the covariance of the uncertainty relations under these operations. The general method is applied to the case of an n-mode system to recover the Sp(2n, R)-covariant multi mode generalization of the single mode Schrödinger-Robertson Uncertainty Principle; and to the set of all polynomials in canonical variables for a single mode system. In the latter situation, the case of the fourth order moments is analyzed in detail, exploiting covariance under the homogeneous Lorentz group SO(2, 1) of which the symplectic group Sp(2, R) is the double cover.