Quantum Obesity: Macro Control & Qubit Correlations

• Quantum obesity is a nonstandard term describing both the extension of quantum control to massive objects and the analytic two-qubit correlation quantifier.
• In the macroscopic context, it involves feedback cooling of a 10 kg oscillator, achieving an 11-order suppression of quantum back-action from thermal noise.
• In quantum information, it is defined via the determinant of the Bloch correlation matrix, serving as an entanglement witness and a marker for phase transitions.

Searching arXiv for papers on "quantum obesity" and closely related usages. Quantum obesity is a nonstandard, context-dependent expression in the arXiv literature. Current usage suggests at least two principal meanings. In an informal macroscopic-mechanics sense, it denotes the extension of quantum-state preparation and control from microscopic systems to very massive, human-scale objects, exemplified by feedback cooling of the center-of-mass motion of a 10 kg Advanced LIGO oscillator to an inferred average phonon occupation $n_{\rm eff}=10.8\pm0.8$. In a formal quantum-information sense, it denotes a two-qubit correlation quantifier, usually abbreviated QO, defined by $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$ from the Bloch correlation matrix and linked to the quantum steering ellipsoid. A related gravitational usage concerns composite quantum bodies whose operator-valued weight is not fixed by internal energy alone (Whittle et al., 2021, Rosario et al., 2023, Lebed, 2012).

1. Terminological scope

The phrase is explicitly described as “not a standard technical term” in the macroscopic-oscillator literature. A plausible implication is that “quantum obesity” functions more as a cross-disciplinary metaphor than as a settled field label. In current arXiv usage, it groups together problems in which quantum structure persists in regimes that are intuitively “too large,” either because the object is macroscopically massive or because the relevant correlation structure exceeds entanglement alone.

Usage	Core object	Representative arXiv paper
Informal macroscopic sense	Near-ground-state control of a 10 kg mechanical oscillator	(Whittle et al., 2021)
Formal QO sense	Two-qubit correlation quantifier $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$	(Rosario et al., 2023)
Relativistic extension	QO, QD, and QSE in a GHS dilaton black-hole setting	(Elghaayda et al., 2024)

This terminological plurality matters because the same expression can refer either to kilogram-scale quantum control or to an analytically computable bipartite correlation measure. The two usages are mathematically unrelated, although both concern the reach of quantum theory beyond familiar microscopic settings.

2. Macroscopic quantum control of massive oscillators

In the macroscopic-mechanics sense, quantum obesity refers to pushing quantum-state preparation into the regime of “very massive, human-scale objects.” The canonical example is the preparation of the differential arm motion of an Advanced LIGO interferometer as a mechanical oscillator with effective mass $10$ kg and natural frequency $\Omega_0 \approx 2\pi\times0.43$ Hz. Active feedback synthesizes an effective trap at $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$ and cools the motion to $n_{\rm eff}=10.8\pm0.8$, corresponding to an effective mode temperature of about $77$ nK from room temperature. The work emphasizes an 11-orders-of-magnitude suppression of quantum back-action by feedback and a 13-orders-of-magnitude increase in the mass of an object prepared close to its motional ground state (Whittle et al., 2021).

The physical motivation is that a mechanical oscillator at room temperature and such a low resonance frequency begins with thermal occupation

$n_{\rm th}\approx \frac{k_B T}{\hbar \Omega},$

which is estimated to be $n_{\rm th}\sim10^{13}$ here. The experiment therefore addresses the regime in which thermal motion would otherwise overwhelm any quantum signature. The relevant zero-point scale is

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$0

while the interferometric displacement imprecision near $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$1–$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$2 Hz is reported as

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$3

corresponding to $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$4 phonons at the relevant frequency scale.

The control protocol is measurement-based feedback. With observed displacement $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$5, the feedback force is chosen as

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$6

so that the effective susceptibility becomes

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$7

The dominant back-action is radiation-pressure shot noise, corresponding to $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$8 phonons of equivalent motion. The experiment is therefore not merely passive cooling; it uses sufficiently strong measurement and sufficiently strong feedback to suppress both thermal motion and measurement back-action. The penalty is feedback back-action from imprecision, described by a term scaling roughly as

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$9

Cooling is quantified from the oscillator mean energy,

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$0

and from the displacement spectrum,

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$1

The inferred minimum occupation $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$2 is identified as about $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$3 ground-state fidelity. In this usage, quantum obesity denotes the claim that a kilogram-scale object is no longer “obviously classical” merely because of its mass.

3. Weight, energy, and composite quantum bodies in gravity

A related gravitational usage concerns quantum bodies whose “mass/weight content” is not sharply determined by internal energy at the operator level. In a weak external gravitational field and in the post-Newtonian approximation, the hydrogen atom provides the simplest composite example. The weak-field metric is

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$4

and the quantized Hamiltonian is written as

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$5

The passive gravitational mass, or weight, operator is

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$6

so the gravitational coupling contains not only the usual internal-energy term but also a virial contribution (Lebed, 2012).

The central result is noncommutativity: $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$7 Therefore, a definite-energy state does not in general have definite weight. This is the microscopic sense in which quantum mechanics complicates classical mass-energy equivalence. The equivalence survives only at the expectation-value level for stationary states, because the quantum virial theorem removes the extra contribution: $\Omega=\vert\det(\mathcal{R})\vert^{1/4}$8

For superpositions of stationary states, the expectation value of weight becomes time dependent. For a two-level superposition, the paper reports an oscillatory term proportional to

$\Omega=\vert\det(\mathcal{R})\vert^{1/4}$9

so that the standard relation between weight and energy is restored only after time averaging: $10$0 The proposed experimental signature is unusual electromagnetic radiation from hydrogen atoms transported at constant velocity in Earth’s field, with excitation probability

$10$1

The estimate given is $10$2, and the authors suggest that for a macroscopic ensemble such as $10$3 moles of hydrogen the emitted photons may be numerous enough to detect. This usage is not identical to the 10 kg-oscillator usage, but it expresses the same broader theme: quantum theory destabilizes classical intuitions about how “large” physical attributes such as weight should behave.

4. Quantum obesity as a geometric correlation quantifier

In quantum information, quantum obesity is a specific analytic function for bipartite two-qubit states. For a Bloch-representation density operator

$10$4

with Bloch correlation matrix $10$5, the quantity is defined as

$10$6

It is directly tied to the quantum steering ellipsoid, whose volume is

$10$7

The quantity is described as capturing quantum correlations beyond entanglement, as being “less restrict than entanglement” but “more restrict than quantum discord,” and as analytically computable for arbitrary two-qubit states (Rosario et al., 2023).

Its operational role is twofold. First, it quantifies a steering-geometry property of the full bipartite state rather than only entanglement. Second, because it is an upper bound for concurrence and because steering ellipsoids can function as entanglement witnesses, QO is used as a witness for entanglement. The emphasis on analyticity distinguishes it from quantum discord, which is often harder to compute.

Closed forms are available for important state families. For the family

$10$8

the paper gives

$10$9

For Bell-diagonal states,

$\Omega_0 \approx 2\pi\times0.43$0

the corresponding expressions are

$\Omega_0 \approx 2\pi\times0.43$1

In this formal sense, quantum obesity is neither metaphorical nor mass-related; it is a determinant-based correlation monotone-like quantity defined on two-qubit states.

5. Quantum critical systems and local filtering

The many-body application of QO is to diagnose quantum phase transitions through pairwise reduced states. The central statement is that $\Omega_0 \approx 2\pi\times0.43$2 is a quantity able to reveal signatures of first-order quantum phase transitions. Because

$\Omega_0 \approx 2\pi\times0.43$3

nonanalyticity in the derivative of the steering-ellipsoid volume can originate from QO itself and/or from the local Bloch-vector factor $\Omega_0 \approx 2\pi\times0.43$4. The authors’ conclusion is that the critical signature is fundamentally rooted in QO (Rosario et al., 2023).

Two models are treated explicitly. The first is the transverse-field Ising-Lenz chain,

$\Omega_0 \approx 2\pi\times0.43$5

with critical point $\Omega_0 \approx 2\pi\times0.43$6. For the reduced two-spin density matrix in the thermodynamic limit, the resulting pairwise quantum obesity is

$\Omega_0 \approx 2\pi\times0.43$7

The derivatives $\Omega_0 \approx 2\pi\times0.43$8 and $\Omega_0 \approx 2\pi\times0.43$9 exhibit an abrupt change at $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$0.

The second model is the anisotropic Heisenberg chain,

$\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$1

with a quantum phase transition at $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$2, between a ferromagnetic phase $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$3 and a gapless phase $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$4. In the Bell-diagonal reduction relevant there, $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$5 because $\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$6 when the local Bloch vector vanishes.

A major methodological result is that local filtering can intensify the critical behavior. For a filtered state

$\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$7

the theorem states

$\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$8

For the Ising-Lenz example, the optimal filters are

$\Omega_{\rm eff}\approx 2\pi\times148~{\rm Hz}$9

with

$n_{\rm eff}=10.8\pm0.8$0

and the filtered derivative contains both $n_{\rm eff}=10.8\pm0.8$1 and $n_{\rm eff}=10.8\pm0.8$2. The reported effect is a stronger abrupt change near the transition point than in the unfiltered quantity.

6. Relativistic and black-hole realizations

The formal QO framework has also been extended to relativistic quantum fields in curved spacetime. One study analyzes QO, quantum discord, and the quantum steering ellipsoid for bipartite Gisin states when Bob’s qubit is subjected to a Garfinkle-Horowitz-Strominger dilaton black hole. The initial state is

$n_{\rm eff}=10.8\pm0.8$3

and the fermionic Hawking structure splits Bob’s mode into Region I and Region II sectors (Elghaayda et al., 2024).

The vacuum takes the two-mode form

$n_{\rm eff}=10.8\pm0.8$4

with

$n_{\rm eff}=10.8\pm0.8$5

where $n_{\rm eff}=10.8\pm0.8$6. QO is again defined from the Bloch correlation matrix as

$n_{\rm eff}=10.8\pm0.8$7

and for the family studied it simplifies to

$n_{\rm eff}=10.8\pm0.8$8

The main findings are region dependent. In Region I, both QD and QO decrease monotonically as the dilaton parameter $n_{\rm eff}=10.8\pm0.8$9 increases; increasing $77$0 tends to increase both quantities, and the QSE expands as $77$1 rises and $77$2 diminishes. In Region II, by contrast, both QD and QO rise from zero and approach finite residual values as $77$3 increases, which the paper attributes to correlation redistribution into the inaccessible sector together with the Pauli exclusion principle and Fermi-Dirac statistics. The QSE there is generally smaller than in Region I, and its dependence on $77$4 is reversed. The combined $77$5 description suggests redistribution rather than simple destruction of quantum correlations.

This relativistic extension preserves the formal, information-theoretic meaning of QO while relocating it to a spacetime setting in which horizon structure, fermionic statistics, and accessibility constraints reshape the observed correlation budget.

7. Distinct non-quantum uses of “obesity”

The phrase quantum obesity should not be conflated with unrelated obesity literatures. One paper on the obesity paradox analyzes collider bias in a structural causal model with binary variables $77$6, $77$7, $77$8, and $77$9, and concludes that collider bias can be the sole cause of the paradox (Viallon et al., 2016). Another treats obesity prevalence as a spatially correlated collective phenomenon with scale-free decay $n_{\rm th}\approx \frac{k_B T}{\hbar \Omega},$0, percolation-like transitions at $n_{\rm th}\approx \frac{k_B T}{\hbar \Omega},$1 and $n_{\rm th}\approx \frac{k_B T}{\hbar \Omega},$2, and a strongly correlated universality class with $n_{\rm th}\approx \frac{k_B T}{\hbar \Omega},$3 (Gallos et al., 2012).

A separate IoT paper proposes WUDI, a human-involved self-adaptive MAPE-H framework for childhood obesity prevention using smartphone and wearable lifelog data, six core predictive features, and a stacking ensemble with CatBoost as meta-learner; it explicitly states that it contains no quantum-related methods, terminology, or concepts (Lee et al., 2023). Another neuroimaging study constructs obesity-associated brain biomarkers from white-matter tract FA statistics in 160 right-handed women from the AOMIC ID1000 dataset, using Wilcoxon rank-sum and FDR-corrected Spearman selection followed by regression and classification models (Suárez-García et al., 2024).

These bodies of work are conceptually and technically distinct from quantum obesity in either the macroscopic-quantum or quantum-information sense. The shared word “obesity” is lexical only. A recurring misconception is therefore to assume that any paper pairing “obesity” with formal mathematics or complex systems is relevant to quantum obesity; the arXiv record does not support that inference.