Certifiable Lower Bounds of Wigner Negativity Volume and Non-Gaussian Entanglement with Conditional Displacement Gates (2403.16441v2)
Abstract: In circuit and cavity quantum electrodynamics devices where control qubits are dispersively coupled to high-quality-factor cavities, characteristic functions of cavity states can be directly probed with conditional displacement (CD) gates. In this Letter, I propose a method to certify non-Gaussian entanglement between cavities using only CD gates and qubit readouts. The CD witness arises from an application of Bochner's theorem to a surprising connection between two negativities: that of the reduced Wigner function, and that of the partial transpose. Non-Gaussian entanglement of some common states, like entangled cats and photon-subtracted two-mode squeezed vacua, can be detected by measuring as few as four points of the characteristic function. Furthermore, the expectation value of the witness is a simultaneous lower bound to the Wigner negativity volume and a geometric measure of entanglement conjectured to be the partial transpose negativity. Both negativities are strong monotones of non-Gaussianity and entanglement, respectively, so the CD witness provides experimentally accessible lower bounds to quantities related to these monotones without the need for tomography on the cavity states.
- S. Haroche, M. Brune, and J. M. Raimond, From cavity to circuit quantum electrodynamics, Nature Physics 16, 243 (2020).
- T. D. Farokh Mivehvar, Francesco Piazza and H. Ritsch, Cavity QED with quantum gases: new paradigms in many-body physics, Advances in Physics 70, 1 (2021).
- R. Simon, Peres-Horodecki Separability Criterion for Continuous Variable Systems, Phys. Rev. Lett. 84, 2726 (2000).
- A. A. Valido, F. Levi, and F. Mintert, Hierarchies of multipartite entanglement for continuous-variable states, Phys. Rev. A 90, 052321 (2014).
- R. Takagi and Q. Zhuang, Convex resource theory of non-Gaussianity, Phys. Rev. A 97, 062337 (2018).
- M. B. Plenio, Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys. Rev. Lett. 95, 090503 (2005).
- U. Chabaud, P.-E. Emeriau, and F. Grosshans, Witnessing Wigner Negativity, Quantum 5, 471 (2021).
- L. G. Lutterbach and L. Davidovich, Method for Direct Measurement of the Wigner Function in Cavity QED and Ion Traps, Phys. Rev. Lett. 78, 2547 (1997).
- H.-W. Lee, Theory and application of the quantum phase-space distribution functions, Physics Reports 259, 147 (1995).
- L. Loomis, An Introduction to Abstract Harmonic Analysis (Van Nostrand, New York, 1953).
- R. Werner, Quantum harmonic analysis on phase space, Journal of Mathematical Physics 25, 1404 (1984).
- A. Kenfack and K. Życzkowski, Negativity of the Wigner function as an indicator of non-classicality, Journal of Optics B: Quantum and Semiclassical Optics 6, 396 (2004).
- P. Jayachandran, L. H. Zaw, and V. Scarani, Dynamics-Based Entanglement Witnesses for Non-Gaussian States of Harmonic Oscillators, Phys. Rev. Lett. 130, 160201 (2023).
- L. Chen, M. Aulbach, and M. Hajdušek, Comparison of different definitions of the geometric measure of entanglement, Phys. Rev. A 89, 042305 (2014).
- M. Khasin, R. Kosloff, and D. Steinitz, Negativity as a distance from a separable state, Phys. Rev. A 75, 052325 (2007).
- R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, 1985).
- J. R. Magnus, On Differentiating Eigenvalues and Eigenvectors, Econometric Theory 1, 179–191 (1985).
- H. Song, G. Zhang, and H. Yonezawa, Strong quantum entanglement based on two-mode photon-subtracted squeezed vacuum states, Phys. Rev. A 108, 052420 (2023).
- A. O. Caldeira and A. J. Leggett, Influence of damping on quantum interference: An exactly soluble model, Phys. Rev. A 31, 1059 (1985).
- T. Hillmann and F. Quijandría, Quantum error correction with dissipatively stabilized squeezed-cat qubits, Phys. Rev. A 107, 032423 (2023).
- J. Eisert, F. G. S. L. Brandão, and K. M. R. Audenaert, Quantitative entanglement witnesses, New Journal of Physics 9, 46 (2007).
- L. M. Johansen, EPR correlations and EPW distributions revisited, Physics Letters A 236, 173 (1997).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010).
- L. Cohen, Wigner Distributions as Representations of the Density Matrix, in Density Matrices and Density Functionals, edited by R. Erdahl and V. H. Smith (Springer Netherlands, Dordrecht, 1987) pp. 305–325.
- J. S. Bell, EPR Correlations and EPW Distributions, Annals of the New York Academy of Sciences 480, 263 (1986).
- While interpretations of Eq. (30) as a probability can be problematic due to the unnormalizability of the EPR state [46], there are no issues here as the only property needed is its positive semidefiniteness.
- R. Hudson, When is the Wigner quasi-probability density non-negative?, Reports on Mathematical Physics 6, 249 (1974).
- F. Soto and P. Claverie, When is the Wigner function of multidimensional systems nonnegative?, Journal of Mathematical Physics 24, 97 (1983).
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