Wigner Functions for Arbitrary Quantum Systems

Tilma, Todd; Everitt, Mark J.; Samson, J. H.; Munro, William J.; Nemoto, Kae

doi:10.1103/physrevlett.117.180401

Cited by 117 publications

(198 citation statements)

References 52 publications

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“…as the displacement of the vacuum state, ñ 0 f | , generating a new coherent state bñ f | . As shown in [23,24], a similar approach to(2) can be used to generate Wigner functions for arbitrary quantum systems. For two-level DV systems, for example,…”

Section: The Wigner Functionmentioning

confidence: 99%

“…where the generalized parity, P â , for a single, two-level, system is s P = + 3 2 a z  (ˆˆ) [23,24,28], for a full derivation of the kernel see [58]. Note that the subscript a here indicates that this is a state for the 'atom', or DV system.…”

Section: The Wigner Functionmentioning

confidence: 99%

“…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].…”

mentioning

confidence: 99%

“…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].…”

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confidence: 99%

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Visualization of correlations in hybrid discrete—continuous variable quantum systems

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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: The Wigner Functionmentioning

confidence: 99%

Section: The Wigner Functionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Visualization of correlations in hybrid discrete—continuous variable quantum systems

et al. 2020

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“…In addition, our method has a great potential in signal analysis. In the future, it will be very interesting to generalize our method to quantum spin systems as Wigner function [18].…”

Section: J Stat Mech (2018) 023113mentioning

confidence: 99%

Quantum phase space with a basis of Wannier functions

Fang

2018

J. Stat. Mech.

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Abstract. A quantum phase space with Wannier basis is constructed: (i)classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and Löwdin method such that each Wannier function is localized at a Planck cell. With these Wannier functions one can map a wave function unitarily onto phase space. Various examples are used to illustrate our method and compare it to Wigner function. The advantage of our method is that it can smooth out the oscillations in wave functions without losing any information and is potentially a better tool in studying quantum-classical correspondence. In addition, we point out that our method can be used for time-frequency analysis of signals.

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Orientational Order Parameters for Arbitrary Quantum Systems

Vrugt

Wittkowski

2020

Annalen der Physik

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The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. This method is generalized to quantum mechanics based on an expansion of Wigner functions. This provides a unified framework applicable to arbitrary quantum systems. The formalism recovers the standard definitions for spin systems. For Fermi liquids, the formalism reveals the nonequivalence of various definitions of the order parameter used in the literature. Moreover, new order parameters for quantum molecular systems with low symmetry are derived, which cannot be properly described with the usual nematic tensors.

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Wigner Functions for Arbitrary Quantum Systems

Cited by 117 publications

References 52 publications

Visualization of correlations in hybrid discrete—continuous variable quantum systems

Visualization of correlations in hybrid discrete—continuous variable quantum systems

Quantum phase space with a basis of Wannier functions

Orientational Order Parameters for Arbitrary Quantum Systems

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