Wigner tomography of multispin quantum states
arXiv:1707.08465 · doi:10.1103/PhysRevA.96.063413
Abstract
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015)]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.
arXiv commentv2: close to published version
References in corpus (23)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Unknown Quantum States and Operations, a Bayesian View
- Discrete phase space based on finite fields
- Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
- Realization of quantum process tomography in NMR
- Experimental quantum compressed sensing for a seven-qubit system
- Quantum computers in phase space
- Wigner Functions for Arbitrary Quantum Systems
- Systematic errors in current quantum state tomography tools
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- A General Theory of Phase-Space Quasiprobability Distributions
- Quantum phase space measurement and entanglement validation made easy
- Visualizing operators of coupled spin systems
- Practical, Reliable Error Bars in Quantum Tomography
- Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
- Experimentally exploring compressed sensing quantum tomography
- Tomographic reconstruction of the Wigner function on the Bloch sphere
- Efficient Quantum State Tomography for Quantum Information Processing using a two-dimensional Fourier Transform Technique
- Complete Reconstruction of the Wavefunction of a Reacting Molecule by Four-Wave Mixing Spectroscopy
- Investigating Bias in Maximum Likelihood Quantum State Tomography
- Error regions in quantum state tomography: computational complexity caused by geometry of quantum states
- Towards a complete, continuous, Wigner function for an ensemble of spins or qubits
- How long does it take to obtain a physical density matrix?
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- Phase-space representation of Landau and electron coherent states for uniaxially strained graphene
- Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
- Visualizing entanglement in atoms and molecules
- Phase Spaces, Parity Operators, and the Born-Jordan Distribution
- Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
- Geometric representation of spin correlations and applications to ultracold systems
- Exploring the mechanisms of qubit representations and introducing a new category system for visual representations: Results from expert ratings
- Wigner State and Process Tomography on Near-Term Quantum Devices
- Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices
- Visualization of correlations in hybrid quantum systems