Overview of the phase space formulation of quantum mechanics with application to quantum technologies
arXiv:2102.11095 · doi:10.1002/qute.202100016
Abstract
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase space is presented. The formulation to generate a generalized phase-space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the asso ciated Q and P functions. Examples of how these different formulations have b een used in quantum technologies are provided, with a focus on discrete quantum systems, qubits in particular. Also provided are some results that, to the authors' knowledge, have not been published elsewhere. These results provide insight into the relation between different representations of phase space and how the phase-space representation is a powerful tool in understanding quantum information and quantum technologies.
arXiv comment42 pages, 4 figures
References in corpus (78)
- Quantum information with continuous variables
- Deformation quantization of Poisson manifolds, I
- Symmetric Informationally Complete Quantum Measurements
- Multi-party entanglement in graph states
- Quantum spin squeezing
- Negativity of the Wigner function as an indicator of nonclassicality
- Stabilizer Codes and Quantum Error Correction
- Contextuality supplies the magic for quantum computation
- Reconstruction of non-classical cavity field states with snapshots of their decoherence
- Direct Fidelity Estimation from Few Pauli Measurements
- Symplectic tomography as classical approach to quantum systems
- Discrete phase space based on finite fields
- Observation of multi-component atomic Schrödinger cat states of up to 20 qubits
- Hudson's Theorem for finite-dimensional quantum systems
- Spin-Nematic Squeezed Vacuum in a Quantum Gas
- Negativity and contextuality are equivalent notions of nonclassicality
- SIC-POVMs and the Extended Clifford Group
- Remote creation of hybrid entanglement between particle-like and wave-like optical qubits
- Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
- Deterministic creation of entangled atom-light Schrödinger-cat states
- Confined quantum Zeno dynamics of a watched atomic arrow
- Quantum computers in phase space
- Toolbox for entanglement detection and fidelity estimation
- Theory of quantum system certification: a tutorial
- Wigner Functions for Arbitrary Quantum Systems
- Generalized Euler Angle Paramterization for SU(N)
- Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
- Contextuality and Wigner function negativity in qubit quantum computation
- Observation of Entanglement Between Itinerant Microwave Photons and a Superconducting Qubit
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- Differential Geometry on SU(3) with Applications to Three State Systems
- A Parametrization of Bipartite Systems Based on SU(4) Euler Angles
- Generalized coherent states for SU(n) systems
- Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem
- Quantum phase space measurement and entanglement validation made easy
- Equivalence between contextuality and negativity of the Wigner function for qudits
- Visualizing operators of coupled spin systems
- Discrete Moyal-type Representations for a Spin
- All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
- Direct Sampling of Negative Quasiprobabilities of a Squeezed State
- Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects
- Monge Distance between Quantum States
- Continuous phase-space representations for finite-dimensional quantum states and their tomography
- Quasiprobability representation of quantum coherence
- Negativity of quasiprobability distributions as a measure of nonclassicality
- Engineering optical hybrid entanglement between discrete- and continuous-variable states
- Quasiprobability and Probability Distributions for Spin 1/2 States
- Split spin-squeezed Bose-Einstein Condensates
- A general approach to quantum mechanics as a statistical theory
- Wigner tomography of multispin quantum states
- Phase-space inequalities beyond negativities
- Negativity volume of the generalized Wigner function as an entanglement witness for hybrid bipartite states
- Quasiprobability distributions for quantum-optical coherence and beyond
- SU(N)-symmetric quasi-probability distribution functions
- Conditional Hybrid Nonclassicality
- Probing nonclassicality with matrices of phase-space distributions
- Wigner process tomography: Visualization of spin propagators and their spinor properties
- Relativistic Wigner Function Approach to Neutrino Propagation in Matter
- Continuous sampling of the squeezed state nonclassicality
- Atomic nonclassicality quasiprobabilities
- Wigner function for SU(1,1)
- Contracting the Wigner-Kernel of a Spin to the Wigner-Kernel of a Particle
- Experimental certification of nonclassicality via phase-space inequalities
- Reconstructing the quantum state of oscillator networks with a single qubit
- Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
- Measurement of complete and continuous Wigner functions for discrete atomic systems
- Revealing quantum correlation by negativity of the Wigner function
- Time evolution of coupled spin systems in a generalized Wigner representation
- Fast computation of spherical phase-space functions of quantum many-body states
- Oscillator state reconstruction via tunable qubit coupling in Markovian environments
- Visualizing entanglement in atoms and molecules
- covariant -parametrized maps
- Phase Spaces, Parity Operators, and the Born-Jordan Distribution
- Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
- Overcoming decoherence in the collapse and revival of spin Schrödinger cats
- On the discrete Wigner function for SU(N)
- On quantum invariants and the graph isomorphism problem
- Some Applications for an Euler Angle Parameterization of SU(N) and U(N)
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- Robust and Deterministic Preparation of Bosonic Logical States in a Trapped Ion
- Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
- Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states
- Simple, reliable and noise-resilient continuous-variable quantum state tomography with convex optimization
- Single-Atom Verification of the Optimal Trade-Off between Speed and Cost in Shortcuts to Adiabaticity
- Quantum speed limits in arbitrary phase spaces
- Phase Spaces, Parity Operators, and the Born-Jordan Distribution
- Mixed discrete variable Gaussian states
- Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
- Quantum and Relativistic corrections to Maxwell-Boltzmann ideal gas model from a Quantum Phase Space approach
- Polytopes of Absolutely Wigner Bounded Spin States
- Navigating the phase diagram of quantum many-body systems in phase space
- Stochastic correction to the Maxwell-Bloch equations via the positive representation
- Parity symmetry breaking of spin- coherent state superpositions in Gaussian noise channel
- Frame representations of qudit quantum mechanics
- Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility
- Grand Unification of All Discrete Wigner Functions on Phase Space
- Enhancing wave-particle duality
- Intensity correlations in the Wigner representation
- Quantum-to-Classical Transition via Single-Shot Generalized Measurements
- Covariant operator bases for continuous variables
- Symmetries and Wigner representations of operational theories
- Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics
- Understanding Squeezed States of Light Through Wigner's Phase-Space
- Benchmarking quantum phase-space methods for near-resonant light propagation
- Third quantization with Hartree approximation for open-system bosonic transport
- Efficient verification and fidelity estimation of discrete bipartite squeezed states