Visualization of correlations in hybrid discrete—continuous variable quantum systems

Ulrik L. Andersen, Jonas Schou Neergaard-Nielsen, Peter van Loock +1 more

Farid Shähandeh

R. P. Rundle, B I Davies, V. M. Dwyer +2 more

Abstract 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 Bell-cat 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.

Yu Meng, Ying Wang, Clara Henke +7 more

Continuous-variable quantum systems are promising candidates for quantum computing and quantum information processing. It is widely known that quadrature measurements on Gaussian continuous-variable systems admit a noncontextual hidden-variable description. Here, we demonstrate that this description fails once the same Gaussian correlations are instead probed using Hadamard tests. We realize the test with a hybrid discrete--continuous-variable system---the polarization and spatial modes of a single photon deterministically generated from an InAs/GaAs quantum emitter, with the controlled operations being the phase-space displacements selected through the Gottesman--Kitaev--Preskill correspondence. By directly measuring the correlations of the operators, we observe a violation of the noncontextual hidden-variable inequality by 380 standard deviations and independently bound the residual noncommutativity of the implemented operations. Our results open up new possibilities for studying fundamental quantum physics using photonic-encoded continuous-variable systems.

R. P. Rundle, B. I. Davies, V. M. Dwyer +2 more

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 within hybrid quantum systems. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bell-cat 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 hybrid quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.

Farid Shähandeh