A qubit maximally entangled with an inaccessible reference is recorded, once per round, by a fresh environment qubit whose two conditional states overlap with amplitude c, and is then rotated by an angle theta about an axis not commuting with the recorded observable. We solve the coherent information I_k = I(R > S_k) exactly for every c, theta and number of rounds k: the Choi spectrum of the k-round channel is Bell-diagonal with eigenvalues (1 +- c^k +- s_1 +- s_2)/4, an even number of minus signs, where s_1 s_2 = c^k and s_1^2 + s_2^2 is a Chebyshev polynomial of the second kind in (1+c) cos(theta) / (2 sqrt c). The consequence we put forward is that a perfect record is not the fastest way to take a qubit's entanglement away. The asymptotic loss rate is maximal at an interior record strength c* = tan^2(pi/4 - theta/2), where it equals artanh(sin theta), the inverse Gudermannian of the rotation angle, against -ln cos(theta) for a perfect record: a factor 2/theta in rate and 0.36/theta in half-life, a factor 7 in rounds at theta = 0.05. The mechanism is critical damping. The damping regimes of this model were classified by Lema et al. (arXiv:2512.14583) in the classical information of the record; what is added here is the reading in coherent information, whose sign decides who can carry the entanglement, with the critical line and both rates in closed form at every angle. Two further exact statements. At theta = pi/2 consecutive records measure complementary observables and the balance is exactly additive, I(R:E) = g(S_Z) + g(S_Y) with g(s) = h_2((1 + e^{-s})/2), so an environment of witnesses becomes an heir once it has spent half a nat of record strength, S = 0.497, split evenly between the two observables. Weak records give a curve that depends on the accumulated strength alone, and the whole family collapses onto three scaling functions with time scales 1/theta^2, 1/theta and 1/s.
A qubit maximally entangled with an inaccessible reference is recorded, once per round, by a fresh environment qubit whose two conditional states overlap with amplitude c, and is then rotated by an angle theta about an axis not commuting with the recorded observable. We solve the coherent information I_k = I(R > S_k) exactly for every c, theta and number of rounds k: the Choi spectrum of the k-round channel is Bell-diagonal with eigenvalues (1 +- c^k +- s_1 +- s_2)/4, an even number of minus signs, where s_1 s_2 = c^k and s_1^2 + s_2^2 is a Chebyshev polynomial of the second kind in (1+c) cos(theta) / (2 sqrt c). The consequence we put forward is that a perfect record is not the fastest way to take a qubit's entanglement away. The asymptotic loss rate is maximal at an interior record strength c* = tan^2(pi/4 - theta/2), where it equals artanh(sin theta), the inverse Gudermannian of the rotation angle, against -ln cos(theta) for a perfect record: a factor 2/theta in rate and 0.36/theta in half-life, a factor 7 in rounds at theta = 0.05. The mechanism is critical damping. The damping regimes of this model were classified by Lema et al. (arXiv:2512.14583) in the classical information of the record; what is added here is the reading in coherent information, whose sign decides who can carry the entanglement, with the critical line and both rates in closed form at every angle. Two further exact statements. At theta = pi/2 consecutive records measure complementary observables and the balance is exactly additive, I(R:E) = g(S_Z) + g(S_Y) with g(s) = h_2((1 + e^{-s})/2), so an environment of witnesses becomes an heir once it has spent half a nat of record strength, S = 0.497, split evenly between the two observables. Weak records give a curve that depends on the accumulated strength alone, and the whole family collapses onto three scaling functions with time scales 1/theta^2, 1/theta and 1/s.
Quantum Darwinism explains why the world agrees about a system: redundant classical records make its pointer observable objective. We ask the complementary question, what it would take for a region of the world to be the continuation of a system rather than a description of it, and organize the answer around one quantity, the coherent information of the history channel from an origin to a region, I(R > X)=S(X)-S(RX) on the Choi state of the dynamics. For a pure global state this is log d minus what the rest of the world knows about the origin, so inheriting is that everybody else be ignorant, and objectivity and individuality are complementary. From this one quantity, three standard facts (strong subadditivity, global purity, data processing) and four ways of cutting the world (space, time, body versus records, and large scale) we obtain the following. Uniqueness of the heir and its causal-clique shape in spacetime; the size of the minimal heir in terms of Darwinian redundancy, with the constant kappa(0.1)=0.026, its form in the currency of recording strength for unequal witnesses, where the bound needs no exchangeability hypothesis, and a shared-secret environment that separates objectivity from heritability; a classification of interactions by degradability, under which pointer interactions never produce an heir. A realization theorem for what two disjoint regions can jointly inherit: their maximal correctable algebras commute, every commuting pair with a multiplicity matrix is realized as the maximal pair of an explicit channel, and what the two regions hold in common is always abelian, of dimension the number of connected components of a bipartite graph that the channel fixes -- so that the shareable part of an ancestry is exactly its classical part. An exact Zeno law for bodies whose dynamics does not commute with what is recorded, whose extended-body form is a classical Markov chain with unistochastic transition matrix and whose criterion is quantum non-demolition, and, for imperfect records, the fact that a perfect record is NOT the fastest way to take a body's identity: the loss is fastest at an interior record strength, where its rate exceeds the perfect-record rate by a factor 2/theta in the rotation angle; a budget inequality under which a lineage that acts on the world spends itself, with a closed frontier for qubits by convexity and a non-convexity for qudits. An existence criterion via information-preserving structures; a de-ordering lemma for biographies in indefinite causal order; and a security formulation in which exclusivity is the privacy of the root's classical record. Most of the physics is other people's and every theorem is attributed in place; Section 1.3 lists one by one what is not, with the realization theorem at the head of that list, and two companion notes carry the two longest proofs. We report, with equal weight, what was tried and fell: a proposed dynamical law of non-inheritance, a dynamical selection of subsystems, and a localization diagnostic, all retracted after adversarial review, and we propose a measurement of the minimal heir on an existing superconducting quantum-Darwinism platform.
If gravity is information, then the gravitational potential must be an amount of information written at a boundary — and it must be written in a way that does not depend on what is on the other side. That is the informational form of the equivalence principle: a potential is universal, indifferent to the composition of what it acts on. This paper puts that requirement on a quantum processor and measures it.This is a follow-up to Gravity as Approach to a Rate–Resolution Bound (doi:10.5281/zenodo.21808410), and reports the hardware campaign that paper did not contain. In the parity–entanglement programme a crossing write changes a region's bias by ⟨P⟩ → ⟨P⟩|cos 2θ|, so that the amount of record it fixes, δS₂ = −ln|cos 2θ|, has the bias cancelled out of it: it is independent of the state of the region written on, and under Φ = −c²δS₂ it is the Newtonian potential, with θ = v_esc/2c. That independence, and not the mere existence of a correlation between regions, is what separates a gravitational potential from an arbitrary entanglement flow, and it is directly testable. We test it with an estimator that is decay-free by construction — the ratio R_ij(θ) = ⟨P⟩_i(θ)/⟨P⟩_j(θ) of two states carried through identical circuits, in which any depolarising factor cancels identically — and we test it against a deliberately introduced violation. On ibm_kingston, across fifteen independent measurements in two jobs, the sector-exchange write shows no drift: χ² = 12.77 on 15 degrees of freedom, p = 0.62, largest deviation 2.3σ. In the same jobs, and with the same estimator, a control write that is state-dependent by construction is resolved at p = 1.1×10⁻²⁰, and its drift is reproduced by a closed form with no fitted parameter at χ²/dof = 0.52, the largest predicted effect (16.74%) being recovered as 16.59%. The conserved membrane ⟨Z_A Z_B⟩ supplies a second, independent discriminator, dropping by 0.007 in the signal arm and by 0.071 in the control. We also report a measured correction to Eq. (3) of the parent paper: the identity ⟨P⟩ = Tr ρ_A² = e^−S₂ holds in the Gaussian sector but not in the qubit sector, where Tr ρ_A² = (1+⟨P⟩²)/2, confirmed tomographically to 0.3%. Exact density-matrix propagation shows the estimator cancels depolarising, dephasing, bit-flip and coherent write-angle error to machine precision, so a miscalibrated write can manufacture neither the null nor a violation; amplitude damping is the sole surviving channel, at 0.11γ. Every number is re-derived offline from the deposited counts by the accompanying script. Statements are labelled [P] proved, [K] known, [N] numerical or measured, [F] formal.
We analyze the angular dependence of the purity-loss rate in a restricted class of open quantum systems: a qubit coupled to a thermal bosonic bath through a commuting interaction operator. Within the Born–Markov approximation, we derive the dissipative generator in closed form andestablish four results. First, the restricted induced trace norm of the generator (on the Hermitian traceless subspace) isindependent of the coupling angle, ‖ℒ(𝐷)𝜃 ‖1→1,ℬ0 = 4𝜋𝜂𝑘𝐵 𝑇,and we give a closed-form proof of this fact based on the rotational structure of the coupling family, together with an independent numerical cross-check.Second, the initial purity-loss rate of a pure reference state depends on the coupling angle through the geometric quantity Γ(𝜃) = |⟨𝜓|𝐴(𝜃)|𝜓⟩|2, which for the qubit family 𝐴(𝜃) = cos 𝜃 𝜎𝑥 + sin 𝜃 𝜎𝑧 takes the exact form Γ(𝜃) = (𝑒𝑥 cos 𝜃 + 𝑒𝑧 sin 𝜃)2. Third, the local curvature of Γ(𝜃) at its maximum defines a curvature-derived angular scale 𝜎geo = 1/√2, universal within this coupling family and independent of every physical parameter of the model; the two forms agree to within ∼ 5% at |𝜃 − 𝜇| = 𝜎geo (Appendix E). Fourth, we quantify explicitly the algebraic (non-exponential) decay of the Markov tail integral for the Ohmic–Lorentzian bath considered here, and we show that a slowly time-dependent coupling angle, 𝜃(𝑡), admits a well-defined adiabatic-Markovian generator; we then prove that the resulting purity-loss functional is not proportional, in general, to the trajectory-integrated Frobenius-norm witness of Ref. [1], identifying the specific obstructions (coherent-precession contamination and a linear-versus-quadratic mismatch in Bloch-vector language) responsible, and we pose as an open problem the narrower question of whether any restricted or reformulated version of the witness admits a well-defined relation to the present results. These results provide an exact microscopic benchmark for trajectory-dependent effective decoherence models: the angular dependence originates from the geometry of the system–environment coupling and the evolving state, not from an intrinsic angular preference of the bath, while a full reduction of the phenomenological model of Ref. [1] to this microscopic setting remains open.