Multi-Operator Quantum Uncertainty Relations from New Cauchy-Schwarz Inequalities

Abstract

We present new generalizations of Cauchy-Schwarz (CS) inequalities to multiple vectors and use them to derive multi-operator quantum uncertainty relations and propose multi-operator squeezing.

16 pages, 6 figures, 1 table, 1 appendix. v2: changed term "M-operator squeezing threshold" to "M-operator variance-product bound" and added term "q/M squeezing threshold" which is actually the 1/Mth power of the new M-operator variance-product bound, due to conceptual benefits from this distinction. Added mixed-state proof in appendix. No results affected

References in corpus (16)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• On the Measurement of Qubits
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Quantum characterization of bipartite Gaussian states
• A Stronger Multi-observable Uncertainty Relation
• Uncertainty relations for general unitary operators
• Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
• Multi-observable Uncertainty Relations in Product Form of Variances
• Variance uncertainty relations without covariances for three and four observables
• Discrete squeezed states for finite-dimensional spaces
• Spin squeezing and entanglement via finite-dimensional discrete phase-space description
• Optomechanical Entanglement of Remote Microwave Cavities
• On the discrete Wigner function for SU(N)
• Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems