Gravitational diffusion in optomechanical probes is conventionally modelled as Markovian white noise, but a finite environmental memory can invalidate the interrogation-time optimisation that underlies precision estimates of the gravitational decoherence rate Λg. We treat the diffusion source as an Ornstein–Uhlenbeck colored-noise channel with memory time τc, generalising the single-mode Gaussian covariance of Souza et al. [arXiv:2602.14841] and recovering the Markovian baseline exactly as τc→0, and evaluate the quantum Fisher information (QFI) for Λg under a fixed total experimental budget including preparation overhead. In the underdamped regime of a feedback-cooled femtogram levitated oscillator, we find that the steady-state QFI is independent of τc, whereas the optimal interrogation time at fixed budget shifts by a factor 15–34 and the QFI rate degrades by up to an order of magnitude as τc grows from the Markovian limit to 0.3 s. A two-parameter Fisher analysis further shows that Λg and τc are nearly degenerate during the transient, so that memory acts as a convergence-rate penalty rather than a precision-ceiling penalty. We stress that this work is a protocol-design and quantum-estimation benchmark, not a near-term detection proposal: even at an effective occupation n̄=50 resolving Λg requires of order 10²⁹–10³⁰ repetitions. All numerical results are illustrative/synthetic benchmarks for a 5 K, 100 kHz femtogram oscillator. I. Introduction Gravitationally induced decoherence [1,2] leaves measurable signatures in the Wigner function of a mechanical probe, and quantum metrology asks how precisely the associated diffusion rate Λg can be inferred. Recent work by Souza, de Sá Neto, Russo, Lo Franco and Adesso [3] established the ultimate quantum-Cramér–Rao sensitivity of a single-mode Gaussian probe to Λg within the Diósi/Kafri–Taylor–Milburn master equation, showing that squeezed-vacuum preparation maximises the transient QFI and that the long-time state is independent of the probe. Their analysis, like essentially all optomechanical decoherence metrology, assumes a delta-correlated (Markovian) environment.
Gravitational diffusion in optomechanical probes is conventionally modelled as Markovian white noise, but a finite environmental memory can invalidate the interrogation-time optimisation that underlies precision estimates of the gravitational decoherence rate Λg. We treat the diffusion source as an Ornstein–Uhlenbeck colored-noise channel with memory time τc, generalising the single-mode Gaussian covariance of Souza et al. [arXiv:2602.14841] and recovering the Markovian baseline exactly as τc→0, and evaluate the quantum Fisher information (QFI) for Λg under a fixed total experimental budget including preparation overhead. In the underdamped regime of a feedback-cooled femtogram levitated oscillator, we find that the steady-state QFI is independent of τc, whereas the optimal interrogation time at fixed budget shifts by a factor 15–34 and the QFI rate degrades by up to an order of magnitude as τc grows from the Markovian limit to 0.3 s. A two-parameter Fisher analysis further shows that Λg and τc are nearly degenerate during the transient, so that memory acts as a convergence-rate penalty rather than a precision-ceiling penalty. We stress that this work is a protocol-design and quantum-estimation benchmark, not a near-term detection proposal: even at an effective occupation n̄=50 resolving Λg requires of order 10²⁹–10³⁰ repetitions. All numerical results are illustrative/synthetic benchmarks for a 5 K, 100 kHz femtogram oscillator. I. Introduction Gravitationally induced decoherence [1,2] leaves measurable signatures in the Wigner function of a mechanical probe, and quantum metrology asks how precisely the associated diffusion rate Λg can be inferred. Recent work by Souza, de Sá Neto, Russo, Lo Franco and Adesso [3] established the ultimate quantum-Cramér–Rao sensitivity of a single-mode Gaussian probe to Λg within the Diósi/Kafri–Taylor–Milburn master equation, showing that squeezed-vacuum preparation maximises the transient QFI and that the long-time state is independent of the probe. Their analysis, like essentially all optomechanical decoherence metrology, assumes a delta-correlated (Markovian) environment.
We develop a comprehensive quantum estimation framework to quantify how precisely gravitationally induced decoherence can be inferred in optomechanical systems, using single-mode Gaussian probe states. Our approach combines a microscopic description of the gravitational diffusion mechanism with quantum Fisher information to determine the ultimate sensitivity achievable in principle. We show that gravitational diffusion leaves distinct, measurable signatures in the mechanical state, both during transient evolution and in the stationary regime. Finally, we identify how probe state preparation shapes the attainable precision, thereby establishing fundamental limits for detecting and estimating gravity-driven decoherence.
We develop a comprehensive quantum estimation framework to quantify how precisely gravitationally induced decoherence can be inferred in optomechanical systems, using single-mode Gaussian probe states. Our approach combines a microscopic description of the gravitational diffusion mechanism with quantum Fisher information to determine the ultimate sensitivity achievable in principle. We show that gravitational diffusion leaves distinct signatures in the mechanical state, both during transient evolution and in the stationary regime. Finally, we identify how probe state preparation shapes the attainable precision, thereby establishing fundamental limits for detecting and estimating gravity-driven decoherence.
A gravitationally induced loss of matter coherence is the most-discussed empirical window on the quantum–gravity interface, and a recurring claim is that its shape — most often a short-time Gaussian onset |ρ₀₁(T)| = e^(−½(T/τ_G)²), as in finite-memory variants of the Diósi–Penrose proposal — diagnoses the underlying mechanism (non-Markovianity, state-dependence, or a genuinely quantum-gravitational record process). We prove the opposite, in a sharp and useful form: the gravitational dephasing curve is mechanism-blind, and the structural distinction that would mark a quantum-gravitational record process is not a function of the reduced channel. Three results, each computed at high precision. (i) The Gaussian onset is not a signature: a state-independent, irreversible record commitment ("seal") firing at a ramping hazard λ(t) = a·t reproduces it exactly (|ρ₀₁(T)| = e^(−aT²/2), residual 0), and a constant hazard gives the pure exponential semigroup — the most Markovian channel there is. (ii) Any state-independent irreversible seal is CP-divisible: |ρ₀₁(T)| = e^(−∫₀ᵀλ) is monotone, so it can never produce revivals; revivals occur exactly for Gaussian kernels whose running integral goes negative — the underdamped (still spectrally positive) kernel is the canonical case, with the boundary at ω₀τ = 3.644173671645632… — a non-Markovianity orthogonal to the structural axis. (iii) Operational undecidability from the dephasing curve: a continuous (Ornstein–Uhlenbeck) classical-noise ontology and a matched sparse-seal record ontology produce bit-identical free-induction coherence |ρ₀₁(T)| for all T (the identity ∫λ_OU = χ is sympy-exact; an independent numerical integration gives the machine-zero residual max|C_OU − C_seal| = 7.1×10⁻¹⁰²), so free-induction decay cannot separate them. Multi-time dynamical decoupling (echo/CPMG) can probe reversibility — it distinguishes a refocusable noise from an irreversible commitment — but the genuine quantum-gravitational content, whether the matter's closed-system record process is indivisible in Barandes' sense / unrefinable in the sealed-record sense, is structural (the off-diagonal support of the decoherence functional between sparse commitments) and is invisible to passive reduced-channel measurement, at every order, because a bath dilation is always divisible and a closed unitary system is indivisible yet a trivial channel (an invasive protocol that reconstructs Γ(t) would insert a seal at each conditioning step, and so cannot certify the unintervened process). We make the structural axis precise, exhibit the consistent-histories functor that turns "unrefinable ⟺ indivisible" into a theorem at the kinematic level, and isolate the one open obligation (whether the gravitational record process is sparsely or continuously sealing). The widely used finite-memory Diósi–Penrose-family kernel is, on this analysis, one illustrative CP-divisible member of the undecidable class rather than a discriminating prediction. The practical upshot is a sharpened no-go: a free-induction onset-shape measurement, however precise, does not distinguish gravitational quantum decoherence from classical gravitational noise — the reversibility of the mechanism is probed only by multi-time decoupling, and the structural indivisibility that would mark a genuinely quantum-gravitational record process is reachable by no reduced-channel measurement at all.
We study quantum gravimetry when the interrogation time carries intrinsic uncertainty, motivated by a fundamental limit on temporal resolution associated with the energy--time uncertainty relation. For linearly gravity-coupled gravimeters, we obtain the effective gravity information by profiling the interrogation time from the two-parameter quantum Fisher information (QFI) matrix. In this class, the time-information block is quadratic in the gravitational parameter, and for quadratic background dynamics, the gravity--time cross term becomes affine in g. These properties yield a normalized expression for the fraction of standard single-parameter gravity QFI that remains once interrogation time is treated as a nuisance parameter, with an affine numerator and a Lorentzian denominator. We work out these results in three benchmark models: a freely falling Gaussian wavepacket, the Kasevich--Chu light-pulse atom interferometer, and an idealized closed-unitary optomechanical model. The Gaussian free-fall benchmark yields an exact closed-form expression for the effective gravity information and shows explicitly how nuisance-time profiling suppresses the momentum-spread-dependent part of the standard single-parameter gravity QFI. In the Kasevich--Chu interferometer, internal state population readout gives a rank-deficient measured two-parameter geometry unless independent timing information is supplied, whereas full access to the final motional and internal states restores a full-rank geometry with retention controlled by the competition between initial velocity spread and gravitationally accumulated motion. In atom-interferometric benchmarks, the framework yields explicit conditions for minimizing nuisance-time information loss, together with corresponding constraints on momentum spread, spatial localization, and long-interrogation-time operation.
Levitated optomechanical systems are approaching the regime where macroscopic quantum superpositions become experimentally accessible. A central question is whether gravity itself, through its unavoidable coupling to material quantum fluctuations, imposes a fundamental decoherence channel on such superpositions. Starting from two independently well-tested physical elements—the quantum vacuum fluctuations of the material energy-momentum tensor, and the weak-field linear response kernel of classical general relativity—we derive a structurally rigid scaling law for the gravitational decoherence rate: \Gamma \propto G M^2 d^2 / (\hbar L^3) \cdot \Phi(l_*/L). The exponents and dependence on mass M, superposition separation d, and object size L are fixed entirely by dimensional analysis and the semiclassical field equations, without tunable parameters. The overall amplitude is set by a single phenomenological input—the ultraviolet cutoff scale l_* of the effective geometric noise. Identifying l_* with the Planck length yields \Phi \sim \mathcal{O}(1) and a decoherence rate of order 1\,\text{Hz} for nanoparticles with M \sim 10^{-14}\,\text{kg}, d \sim 10^{-7}\,\text{m}, and L \sim 10^{-6}\,\text{m}, placing the prediction within the foreseeable sensitivity window of next-generation levitated optomechanical setups. We provide explicit falsification conditions, a three-path staged verification strategy that does not require simultaneous optimisation of all parameters, and operational signatures—including a distinctive pure-dephasing channel without energy relaxation—that distinguish this mechanism from environmental noise, zero-temperature electromagnetic vacuum fluctuations, and the Diósi-Penrose model.
We study the metrological extractability of a relative gravitational-redshift parameter delta encoded in Page–Wootters (PaW) historical states of a clock C and a two-level probe S. Writing the redshifted history state as |Psi(delta)> = exp(-i delta G)|Psi(0)>, with G = dt sum_n n |n><n| (x) H_S, we obtain the exact finite-N quantum Fisher information F_Q = (omega_0 dt)^2 (N-1)(2N-1)/6 tending to (omega_0 T)^2/3 in the continuous limit. Two results follow. First, F_Q vanishes for separable clock-probe states, so that a non-zero joint quantum Fisher information for the relative redshift is equivalent to C–S entanglement entering the correlations; separable-state redshift dynamics, present in earlier PaW treatments, nevertheless survives without providing any joint estimability. Second, a deterministic protocol that reads the clock record n and then performs Ramsey readout on S attains the joint QFI exactly, with no post-selection overhead, yielding a factor ~26 advantage over measuring the reduced probe alone for our toy model. With state-of-the-art optical-lattice clocks (Sr-87, T = 1 s), a 1 m height difference becomes resolvable in tens of shots, placing the PaW resource picture in the same regime as cm-scale clock-array experiments. We contrast this with history-state fidelity, a basis-dependent diagnostic, and discuss decoherence, GHZ scaling and an error budget.