Quantum trajectories — the stochastic pure-state evolutions of an individually monitored open system — differ for every detection scheme (unravelling) that reproduces the same master equation, but no experiment has ever established whether these jumps are objective properties of the system or artifacts of how the environment is monitored. Wiseman and Gambetta (Phys. Rev. Lett. 108, 220402 (2012)) turned this into an operational question: they defined the class of objective pure-state dynamical models (OPDMs) — models in which the system has a real pure state whose stochastic evolution exists independent of any detection scheme — constructed an EPR-steering test between Alice's monitoring record of a driven atom's fluorescence and Bob's independent tomography, and proved that all OPDMs satisfy a steering parameter bound S ≤ 1. Realizing this test experimentally, without loopholes, remains unachieved: the original protocol requires total detection efficiency η ≳ 0.58 (adaptively detected spectrally resolved photon counting plus homodyne) or η ≳ 0.73 (homodyne only), feedback faster than the atomic lifetime, detector bandwidth far exceeding the Rabi drive, and a rigorously closed efficiency-accounting loophole; subsequent theory lowered the sufficient threshold to ηc ≈ 0.37 for idealized adaptively switched jump schemes and proved η > 1/2 a hard floor for any pair of diffusive monitorings, while the best monitored-emitter experiments reach η ≈ 0.3–0.33 with a single unravelling and no steering analysis. The open problem is the complete experimental realization: implementing at least two run-by-run selectable unravellings of the same system, closing all practical loopholes, and demonstrating a statistically significant violation S > 1, thereby refuting all OPDMs and establishing that quantum jumps are detector-dependent.

Background

When an open quantum system is continuously monitored through its environment, its state, conditioned on the measurement record, follows a stochastic pure-state path called a quantum trajectory. Averaged over all records the evolution is the usual Markovian master equation; any monitoring scheme that reproduces the same master equation when its record is ignored is called an unravelling of that master equation. Different unravellings — for example photon counting, which produces discrete quantum jumps, and homodyne detection, which produces continuous diffusive state spread — are empirically distinguishable in their conditioned trajectories even though they agree on all unconditional dynamics. This poses a foundational question: is the stochastic pure-state evolution of an individual system an objective property, or is it defined only relative to the detector? Wiseman and Gambetta (2012) gave this a precise operational form. They defined an objective pure-state dynamical model (OPDM) as any model in which the system has a genuine (observer-independent) pure state at all times whose stochastic evolution is unaffected by how the environment is monitored. To refute all OPDMs they constructed a test based on EPR steering — the operational notion of steering (formalized by Wiseman, Jones and Doherty in 2007 as a quantum information task with a trusted-party hierarchy between entanglement witnessing and Bell nonlocality) in which one party's measurement choices nonlocally determine the conditional state of the other party's system. The protocol: a two-level atom resonantly driven with Rabi frequency Ω and radiative decay rate γ; in each run Alice randomly chooses one of two monitorings of the emitted fluorescence — SAID, i.e. spectrally resolved photon counting with a weak local oscillator whose phase flips after each detection (valid in the Ω/γ → ∞ limit), and Y-quadrature homodyne detection — while Bob, ignorant of her choice, tomographically measures one of σx, σy, σz at a randomly chosen time after transients. Alice bins Bob's outcomes according to labels computed from her monitoring record; the binned statistics define a steering parameter S such that every OPDM obeys S ≤ 1. A violation S > 1 therefore refutes all OPDMs, establishing that the jumps or diffusion an observer sees are detector-dependent rather than objective properties of the atom. The obstruction is detection efficiency: η, the total fraction of emitted fluorescence actually detected (light collection, propagation, and detector quantum efficiency combined), must satisfy the necessary conditions η_S + η_Y > 1 (so η > 1/2 at equal efficiencies) — a bound that later work proved necessary for any pair of purely diffusive unravellings. Sufficient thresholds computed by the authors are η ≳ 0.58 for the SAID+Y pair and η ≃ 0.73 for an X+Y homodyne pair, with additional hardware demands: feedback faster than γ⁻¹ and spectral resolution in the Ω ≫ γ regime for SAID, and detector effective bandwidth much greater than Ω for homodyne, since the homodyne photocurrent spectrum carries signals at 0 and ±Ω.

Problem Statement

Realize, experimentally and loophole-free, the Wiseman–Gambetta EPR-steering test that decides whether dynamical quantum jumps are objective or detector-dependent. Concretely, on a monitored open system (paradigmatically a driven two-level emitter with Rabi frequency Ω and decay rate γ): (1) implement at least two genuinely distinct unravellings of the same master equation, selectable randomly run-by-run — such as adaptively detected spectrally resolved photon counting (SAID) and quadrature homodyne detection, or any improved pair — with the feedback latency, spectral resolution, and detector bandwidth the schemes demand (feedback faster than γ⁻¹ and resolution in the Ω ≫ γ regime for SAID; effective bandwidth ≫ Ω for homodyne); (2) acquire Alice's monitoring records and Bob's independent, randomly chosen tomographic measurements of the system, and demonstrate a statistically significant violation of the steering inequality S ≤ 1 that every objective pure-state dynamical model must satisfy, with total detection efficiency η (collection, propagation, and detector quantum efficiency combined) above the threshold the implemented pair requires; and (3) close the practical loopholes so the violation cannot be attributed to experimental artifacts: all loss channels monitored or bounded, the fraction of fluorescence sent to Alice well characterized, and Bob's readout free of correlated biases. The investigation jointly includes the design of optimized, experimentally realistic monitoring pairs and steering inequalities that minimize the required efficiency under realistic imperfections — a supporting deliverable, not an alternative completion. The completion boundary is the loophole-free experimental violation itself: a demonstrated S > 1 (or an equivalent steering violation proven to bound all OPDMs for the implemented monitorings) that no objective pure-state dynamical model can reproduce, thereby establishing experimentally that quantum trajectories are detector-dependent.

References

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