Harvesting Contextuality from the Vacuum

TL;DR

The paper explores whether quantum contextuality can be harvested from the vacuum using Unruh-DeWitt probes coupled to a massless scalar field in 3+1 Minkowski space. It formalizes harvesting via the sheaf-theoretic framework and the contextual fraction, introducing genuine harvesting criteria to distinguish field-origin nonclassicality from signaling. Results show that a single qutrit can harvest contextuality from vacuum, including gapless regimes for specific measurement settings, and that a qubit-qutrit system can exhibit coexistence and tradeoffs between contextuality and entanglement, with explicit density-matrix decompositions highlighting how field correlations drive nonclassicality. The work lays a foundation for extensions to fully relativistic and nonperturbative treatments, curved spacetimes, and applications to relativistic quantum information protocols.

Abstract

Quantum contextuality is the notion that certain measurement scenarios do not admit a global description of their statistics and has been implicated as the source of quantum advantage in a number of quantum information protocols. It has been shown that contextuality generalizes the concepts of non-local entanglement and magic, and is an equivalent notion of non-classicality to Wigner negativity. In this paper, the protocol of contextuality harvesting is introduced and it is shown that Unruh-DeWitt models are capable of harvesting quantum contextuality from the vacuum of a massless scalar quantum field. In particular, it is shown that gapless systems can be made to harvest contextuality given a suitable choice of measurements. The harvested contextuality is also seen to behave similarly to harvested magic and can be larger in magnitude for specific parameter regimes. An Unruh-DeWitt qubit-qutrit system is also investigated, where it is shown that certain tradeoffs exist between the harvested contextuality of the qutrit and the harvested entanglement between the systems, and that there are harvesting regimes where the two resources can both be present. Some of the tools of contextuality, namely the contextual fraction, are also imported and used as general harvesting measures for any form of contextuality, including non-local entanglement and magic. Additionally, new criteria for genuine harvesting are put forward that also apply to individual systems, revealing new permissible harvesting parameter regimes.

Figures (2)

• Figure 1: Plots for the single qutrit harvesting scenarios. The first three columns of plots depict $\Delta CF(\bm v^e)/\lambda^2$ with solid curves and $M(\hat{\rho})/\lambda^2$ with dot-dashed curves, while the last depicts $|\Delta(\Lambda_d^{+}, \Lambda_{d}^{+})|$ with dotted curves and $|H(\Lambda_d^{+}, \Lambda_{d}^{+})|$ with dashed curves, all as functions of the energy gap $\Omega$ for different temporal smearing widths and a coupling constant of $\lambda = 10^{-4}$. The top plots correspond to a spatial smearing width of $(\alpha_{1_1})^{-1/2} = 1$, while the bottom plots correspond to $(\alpha_{1_1})^{-1/2} = 0.1$. All plots additionally consider $\bar{t}_d=0$. The columns of the first three columns of plots represent the 3 sets of angles for the scenarios introduced in Appendix \ref{['Appendix:QutritContextScenario']}, with the order of the columns following the order of appearance of the sets of angles.
• Figure 2: Plots for the qubit-qutrit harvesting scenario. The plots in the left column depict $\mathcal{N}(\hat{\rho}_D(t))/\lambda^2$ with solid curves, while the plots in the right column depict $|\Delta(\Lambda_d^{+}, \Lambda_{d'}^{+})|$ with dotted curves and $|H(\Lambda_d^{+}, \Lambda_{d'}^{+})|$ with dashed curves, all as functions of the energy gap $\Omega_d=\Omega_{d'}$ for different temporal smearing widths and a coupling constant of $\lambda_d = 10^{-4}$; all plots have $\bar{t}_d=0$ additionally. The first and third rows denote spatial smearing widths of $(\alpha_{1_1})^{-1/2} = 1$, while the second and third denote $(\alpha_{1_1})^{-1/2} = 0.1$. Finally, the first two rows correspond to a separation of $L_{l_dm_{d'}}=1/2$, while the last two correspond to $L_{l_dm_{d'}}=3$.