Phase-space noncommutative formulation of Ozawa's uncertainty principle
arXiv:1406.0740 · doi:10.1103/PhysRevD.90.045023
Abstract
Ozawa's measurement-disturbance relation is generalized to a phase-space noncommutative extension of quantum mechanics. It is shown that the measurement-disturbance relations have additional terms for backaction evading quadrature amplifiers and for noiseless quadrature transducers. Several distinctive features appear as a consequence of the noncommutative extension: measurement interactions which are noiseless, and observables which are undisturbed by a measurement, or of independent intervention in ordinary quantum mechanics, may acquire noise, become disturbed by the measurement, or no longer be an independent intervention in noncommutative quantum mechanics. It is also found that there can be states which violate Ozawa's universal noise-disturbance trade-off relation, but verify its noncommutative deformation.
References in corpus (35)
- String Theory and Noncommutative Geometry
- Noncommutative Field Theory
- Quantum Field Theory on Noncommutative Spaces
- Noncommutative Geometry and Matrix Theory: Compactification on Tori
- Noncommutative Field Theory and Lorentz Violation
- Noncommutative geometry inspired Schwarzschild black hole
- D-branes and the Noncommutative Torus
- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
- Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements
- Noncommutative Gravitational Quantum Well
- Proof of Heisenberg's error-disturbance relation
- How well can one jointly measure two incompatible observables on a given quantum state?
- Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement
- Joint quantum measurements with minimum uncertainty
- Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
- Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements
- Measurement uncertainty relations
- Noncommutative field theory and violation of translation invariance
- Black Holes and Phase Space Noncommutativity
- Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations
- Wigner Measures in Noncommutative Quantum Mechanics
- Position measuring interactions and the Heisenberg uncertainty principle
- Entanglement due to noncommutativity in the phase-space
- Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
- A universally valid Heisenberg uncertainty relation
- The singularity problem and phase-space noncanonical noncommutativity
- Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle
- Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
- The -value Equation and Wigner Distributions in Noncommutative Heisenberg algebras
- A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
- Can noncommutative effects account for the present speed up of the cosmic expansion?
- What kind of noncommutative geometry for quantum gravity ?
- Heisenberg's uncertainty relation: Violation and reformulation
- Noncommutative Double Scalar Fields in FRW Cosmology as Cosmical Oscillators
- Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
Cited by in corpus (24)
- Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
- Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
- Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
- Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane
- Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
- Quantum speed limit for a relativistic electron in the noncommutative phase space
- Klein-Gordon theory in noncommutative phase space
- Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
- Gaussian fidelity distorted by external fields
- Coherent quantum squeezing due to the phase space noncommutativity
- Quantum cloning and teleportation fidelity in the noncommutative phase-space
- Classical and statistical limits of the quantum singular oscillator
- Phase-space elementary information content of confined Dirac spinors
- Relativistic dispersion relation and putative metric structure in noncommutative phase-space
- Collapsing Shells and Black Holes: a quantum analysis
- Quantum information aspects of noncommutative quantum mechanics
- Entanglement and separability in the noncommutative phase-space scenario
- Error-disturbance uncertainty relations in Faraday measurements
- Path-integral action of a particle in the noncommutative phase-space
- A Phase-Space Noncommutative Picture of Nuclear Matter
- Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
- Emergent time crystals from phase-space noncommutative quantum mechanics
- Test of Space-Time Non-Commutativity at the Future Circular Collider
- Noncommutative Classical Dynamics on Velocity Phase Space and Souriau Formalism