Quantum-jump determination of current fluctuations under imperfect detection

Determine whether steady-state current fluctuations in the non-additive master equation for a two-site fermionic network coupled to two independent thermal reservoirs can be computed exactly using a quantum-jump unravelling under imperfect detection, including unravellings in alternative bases or forms such as non-Markovian, diffusive, partially observed, or correlated-jump unravellings, and whether the corresponding fluctuations can be experimentally measured.

Background

The paper studies a double quantum dot governed by a non-additive quantum master equation whose dissipator contains cross terms arising from interference between two thermal reservoirs. The authors show that additive quantum-jump unravellings associated with perfect detection of local or global jumps generally fail: their no-jump evolution is not completely positive, and their predicted current fluctuations disagree with the Landauer–Büttiker result.

For imperfect detection, some local additive unravellings can reproduce the Landauer–Büttiker current and fluctuations while maintaining complete positivity of the no-click map in suitable parameter regimes, particularly at sufficiently high temperatures. However, the authors do not establish whether other measurement schemes—such as non-Markovian, diffusive, partially observed, coarse-grained, or correlated-jump unravellings—can provide exact current-fluctuation statistics generally, nor whether these statistics can be realized experimentally. This unresolved question is therefore explicitly identified as an open problem.

References

Since a particular additive unravelling corresponds to a specific measurement scheme, it remains unclear whether unravelling the non-additive master equation in some other basis or manner, for example, via a non-Markovian unravelling, a diffusive unravelling, a partially observed unravelling when the detector only accesses a coarse-grained charge signal, or via an unravelling with correlated quantum jumps -- and thus performing the associated measurement, for instance, via rf reflectometry -- would enable the exact determination of the current fluctuations when some jumps go undetected. In this regard, it is still an open question whether one can compute steady-state current fluctuations using the quantum jump approach under imperfect detection and perform their experimental measurement.

— Current fluctuations in a non-additive open quantum system: breakdown of the quantum-jump approach  (2608.14469 - Khomchenko et al., 14 Aug 2026) in Section Discussion and Concluding Remarks