Quasiprobability representation of quantum coherence

Sperling, Jan

doi:10.1103/physreva.97.062327

Cited by 46 publications

(67 citation statements)

References 116 publications

(148 reference statements)

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“…Quantifying different types of correlations in quantum systems is a key area of research that has received a great deal of attention [62][63][64][65][66][67][68][69]. In parallel, phase-space methods have been utilized as a tool to identify and categorize quantum correlations [41,[70][71][72][73]. Further, these methods have been used to generate measures based on the emergence of negative quasi-probabilities in the Wigner function [37,[74][75][76].…”

Section: Visualizing Correlations In Hybrid Quantum Systemsmentioning

confidence: 99%

Visualization of correlations in hybrid discrete—continuous variable quantum systems

et al. 2020

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In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bellcat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.Bloch sphere [20][21][22][23][24][25][26]. For example, there have been various proposals put forward that use a continuous Wigner function to reveal correlations between DV systems [26][27][28]. These methods have further been validated through the direct measurement of phase-space to reveal quantum correlations [28][29][30][31]. Recently this has been extended to experiments validating atomic Schrödinger cat states of up to 20 superconducting qubits [32].A case that has not been explored in much detail is the phase-space representation of CV-DV hybridization. This hybridisation is seen in many applications of quantum technologies, including simple gate models for quantum computers, such as hybrid two-qubit gates [33,34], and CV microwave pulse control of DV qubits [35]. The generation of hybrid quantum correlations within CV-DV hybrid 5 systems commonly takes place within the framework of cavity quantum electrodynamics, that describes the interaction between a two-level quantum system and a single mode of a microwave field. These models can be further used to describe the effect of circuit quantum electrodynamics, and to consider the interaction of the microwave field with an artificial atom. Analyzing these interactions within the framework of the Jaynes-Cummings model [36] allows us to display how quantum information is shared between the CV and DV systems.A number of papers [23, 24, 37] have shown the mathematical construction of hybrid states within the phase space, these have been constructed without giving a way to visually display the degrees of freedom of such composite systems. A method for displaying states with heterogeneous degrees of freedom, using the Wigner function, came from the application of composite phase-space methods to quantum chemistry [38]. The technique presented here is based on this approach, however in [38], reduced Wigner functions are used and an envelope is further applied, potentially losing many o...

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Section: Visualizing Correlations In Hybrid Quantum Systemsmentioning

confidence: 99%

Visualization of correlations in hybrid discrete—continuous variable quantum systems

et al. 2020

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“…Mostly independently from the development of the entanglement theory, the notion of quasiprobabilities was devised by Wigner [9] and others; see Ref. [10] for a thorough introduction. In particular, the nonclassicality in a single optical mode can be visualized through negativities in this distribution which cannot occur for classical light.…”

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confidence: 99%

“…Still, the benefit of EQPs is that negativities in them allow for a necessary and sufficient identification of entanglement. Moreover, EQPs apply to discrete-and continuous-variable systems as well as in the multimode scenario beyond bipartite systems [10,24], enabling the theoretical characterization of a manifold of differently entangled states. Despite the theoretically predicted advantages of EQPs, to date, EQPs have not been reconstructed in any experiment.…”

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Experimental Reconstruction of Entanglement Quasiprobabilities

et al. 2019

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We report on the first experimental reconstruction of an entanglement quasiprobability. In contrast to related techniques, the negativities in our distributions are a necessary and sufficient identifier of separability and entanglement and enable a full characterization of the quantum state. A reconstruction algorithm is developed, a polarization Bell state is prepared, and its entanglement is certified based on the reconstructed entanglement quasiprobabilities, with a high significance and without correcting for imperfections. arXiv:1810.07040v2 [quant-ph]

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Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Rundle

Everitt

2021

Adv Quantum Tech

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The phase‐space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including methods 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 associated Q and P functions. Examples of how these different formulations are 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.

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Quasiprobability representation of quantum coherence

Cited by 46 publications

References 116 publications

Visualization of correlations in hybrid discrete—continuous variable quantum systems

Visualization of correlations in hybrid discrete—continuous variable quantum systems

Experimental Reconstruction of Entanglement Quasiprobabilities

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

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