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Resource efficient certification of system environment entanglement solely from reduced system dynamics

Jhen-Dong Lin, Pao-Wen Tu, Kuan-Yi Lee, Neill Lambert, Adam Miranowicz, Franco Nori, Yueh-Nan Chen

TL;DR

This work addresses certifying system–environment entanglement in open quantum systems with inaccessible environments by introducing non-mixed unitarity (NMU), a witness based on mixed-unitary channels that applies to general non-autonomous pure dephasing dynamics. The authors establish that a reduced map that is not MU signals entanglement generation with the environment, and they provide an NMU-based measure $Q_A$ derived from the Choi state to quantify this effect. Compared with Hamiltonian-ensemble incompatibility, NMU relaxes the autonomy requirement, reduces the need for full-time dynamics, and allows entanglement certification at arbitrary times, even from short-time dephasing regimes. They validate the approach experimentally on a trapped-ion processor and discuss applications to gravitationally induced entanglement, demonstrating practical resource advantages and potential for fundamental tests of gravity-induced quantum correlations.

Abstract

Certifying nonclassical correlations typically requires access to all subsystems, presenting a major challenge in open quantum systems coupled to inaccessible environments. Recent works have shown that, in autonomous pure dephasing scenarios, quantum discord with the environment can be certified from system-only dynamics via the Hamiltonian ensemble formulation. However, this approach leaves open whether stronger correlations, such as entanglement, can be certified. Moreover, its reliance on Fourier analysis requires full-time dynamics, which is experimentally resource-intensive and provides limited information about when such correlations are established during evolution. In this work, we present a method that enables the certification of system-environment quantum entanglement solely from the reduced dynamics of the system. The method is based on the theory of mixed-unitary channels and applies to general non-autonomous pure dephasing scenarios. Crucially, it relaxes the need for full-time dynamics, offering a resource-efficient approach that also reveals the precise timing of entanglement generation. We experimentally validate this method on a Quantinuum trapped-ion quantum processor with a controlled-dephasing model. Finally, we highlight its potential as a tool for certifying gravitationally induced entanglement.

Resource efficient certification of system environment entanglement solely from reduced system dynamics

TL;DR

This work addresses certifying system–environment entanglement in open quantum systems with inaccessible environments by introducing non-mixed unitarity (NMU), a witness based on mixed-unitary channels that applies to general non-autonomous pure dephasing dynamics. The authors establish that a reduced map that is not MU signals entanglement generation with the environment, and they provide an NMU-based measure derived from the Choi state to quantify this effect. Compared with Hamiltonian-ensemble incompatibility, NMU relaxes the autonomy requirement, reduces the need for full-time dynamics, and allows entanglement certification at arbitrary times, even from short-time dephasing regimes. They validate the approach experimentally on a trapped-ion processor and discuss applications to gravitationally induced entanglement, demonstrating practical resource advantages and potential for fundamental tests of gravity-induced quantum correlations.

Abstract

Certifying nonclassical correlations typically requires access to all subsystems, presenting a major challenge in open quantum systems coupled to inaccessible environments. Recent works have shown that, in autonomous pure dephasing scenarios, quantum discord with the environment can be certified from system-only dynamics via the Hamiltonian ensemble formulation. However, this approach leaves open whether stronger correlations, such as entanglement, can be certified. Moreover, its reliance on Fourier analysis requires full-time dynamics, which is experimentally resource-intensive and provides limited information about when such correlations are established during evolution. In this work, we present a method that enables the certification of system-environment quantum entanglement solely from the reduced dynamics of the system. The method is based on the theory of mixed-unitary channels and applies to general non-autonomous pure dephasing scenarios. Crucially, it relaxes the need for full-time dynamics, offering a resource-efficient approach that also reveals the precise timing of entanglement generation. We experimentally validate this method on a Quantinuum trapped-ion quantum processor with a controlled-dephasing model. Finally, we highlight its potential as a tool for certifying gravitationally induced entanglement.
Paper Structure (11 sections, 2 theorems, 52 equations, 4 figures)

This paper contains 11 sections, 2 theorems, 52 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Certify system-environment entanglement of pure dephasing
  3. Comparison with Hamiltonain ensemble formalism
  4. Experiment on cloud quantum computer
  5. Witnessing gravitationally induced entanglement
  6. Discussion and Conclusion
  7. Formal proof of Theorem 1
  8. Corrected qutrit-like conditions
  9. Formal proof of Theorem 2 with corrected qutrit-like criteria
  10. Conjecture: estimating negativity by non-mixed unitarity
  11. Circuit decomposition of the controlled-controlled rotation gate

Key Result

Theorem 1

The reduced evolution of a system is a mixed-unitary channel if the evolved system-environment state $\rho_{\text{S}\text{E}}$ remains zero-discordant from E to S.

Figures (4)

  • Figure 1: (a) Circuit implementation of a pure dephasing dynamics governed by Eq. \ref{['eq: Hamiltoninan with single qubit environment']}, where we set $\theta =2t$. (b) Theoretical (blue curve) and experimental (red triangles) results for the NMU measure $Q_A$ as a function of time. (c) The fitting curve (blue curve) and the experimental data (red triangles) for the dephasing factor $\Im[\phi_{01,11}(t)]$. (d) Comparison of the theoretical distribution $\chi(\omega)$ (solid blue curve) and the reconstructed distribution $\chi_\text{fit}(\omega)$ (red dashed curve).
  • Figure 2: Schematic illustration of gravitational interaction between test particles and a mechanical oscillator.
  • Figure 3: Negativity of the system-environment state [Eq. \ref{['eq: negativity']}] verses the NMU measure $Q_\text{A}$ for (a) $d_\text{S} = 3$ and (b) $d_\text{S}=4$ with randomly sampled pure dephasing maps.
  • Figure 4: Circuit decomposition of a CCRZ gate with $\alpha = \theta/4$.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof