Overview of the phase space formulation of quantum mechanics with application to quantum technologies

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.

42 pages, 4 figures

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Cited by in corpus (5)

• New Phase Space Formulations and Quantum Dynamics Approaches
• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states
• Relating the Glauber-Sudarshan, Wigner and Husimi quasiprobability distributions operationally through the quantum limited amplifier and attenuator channels
• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• Efficient verification and fidelity estimation of discrete bipartite squeezed states