Entanglement-Suppression Conjecture

• The Entanglement-Suppression Conjecture is a family of principles that constrain dynamics by reducing entanglement generation, particularly in low-energy hadronic interactions.
• It employs specific criteria—such as the S-matrix being proportional to the Identity or SWAP operator—to enforce phase-shift degeneracies that yield enhanced emergent symmetries.
• The conjecture spans diverse domains, impacting fields from hadron physics and noisy quantum circuits to quantum information theory, and motivates further experimental and theoretical investigation.

The Entanglement-Suppression Conjecture denotes a family of conjectural principles in which reduced entanglement generation is treated as an organizing constraint on dynamics. In its most technically developed hadronic form, the conjecture states that low-energy hadronic interactions may dynamically prefer two-body scattering processes whose $S$-matrix generates as little bipartite entanglement as possible; in the strongest formulation adopted in recent work, this means vanishing entanglement power for all incoming product states, which is equivalent to the $S$-matrix being proportional to either the Identity or the SWAP operator on the relevant bipartite Hilbert space (Hu et al., 30 Jul 2025). Other literatures use the same phrase for distinct ideas, including noisy scrambling dynamics, nonlinear collapse models, disentangler channels, and topological or holographic constraints on multipartite entanglement, so the term names a research program rather than a single universally accepted theorem.

1. Meanings and scope

Across current literature, “entanglement suppression” does not have a unique definition. In low-energy hadron physics it refers to suppression of scattering-induced bipartite entanglement and is tied to emergent spin-flavor symmetry (Beane et al., 2018). In noisy quantum circuits it refers to the regime in which stronger scrambling reduces residual mixed-state entanglement because dephasing destroys the coherence needed to sustain delocalized information (Haas et al., 2024). In foundations it can denote a nonlinear dynamics that drives bipartite pure states toward product states and is proposed as a collapse mechanism (Buks, 2023). In quantum complexity theory it appears in the theory of disentanglers, where one asks whether a channel can map large inputs to states close to separable outputs without exponentially large resources (Jeronimo et al., 2024).

Domain	Operative meaning of suppression	Representative papers
Low-energy hadron scattering	Vanishing or minimal entanglement power of the two-body $S$-matrix	(Beane et al., 2018, Hu et al., 30 Jul 2025, Hu et al., 10 Jun 2025)
Noisy scrambling circuits	Dephasing turns scrambling from entanglement-generating to entanglement-reducing	(Haas et al., 2024)
Nonlinear quantum dynamics	Added nonlinear term suppresses bipartite entanglement and favors product states	(Buks, 2023)
Disentangler theory	Channels output states close to separable states only under strong structural promises, or require exponential input size	(Jeronimo et al., 2024, Akibue et al., 2024)
Topological/holographic uses	Exact factorization, manifold-labeled multipartite structure, or saturation of growth in mixed-state settings	(Chun et al., 2017, Zotto et al., 18 Feb 2026, Momeni, 12 Sep 2025)

This multiplicity matters conceptually. Some versions concern dynamical minimization of entanglement generation, others concern hardness of removing entanglement, and still others concern constraints on which multipartite structures can survive in the infrared. A plausible implication is that the conjecture is best understood as a family resemblance among several programs rather than a single cross-disciplinary statement.

2. Hadronic minimal-entanglement formulation

The most explicit formulation treats two-body scattering as a quantum-information process. For distinguishable particles with incoming product state

$$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$

the outgoing state is

$$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$

Entanglement can be quantified from the reduced density matrix $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$, using for example the von Neumann entropy

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$

or the linear entropy

$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$

Recent hadronic work avoids explicit averaging by using a theorem for two qudits: an operator maps every product state to another product state iff it is proportional to either the Identity or the SWAP operator. The precise minimal-entanglement criterion is therefore that the two-body $S$-matrix be proportional to $1$ or $S$0 on the bipartite space chosen for the entanglement analysis (Hu et al., 30 Jul 2025).

For two equal-spin particles of spin $S$1, the spin-space scattering matrix is decomposed as

$S$2

where $S$3 projects onto total spin $S$4. Because

$S$5

the Identity condition gives

$S$6

Using the exchange symmetry of the $S$7-channels, the SWAP condition becomes equality among all odd-$S$8 phases and among all even-$S$9 phases, with the two classes differing by $S$0: $S$1 with

$S$2

In this framework, the conjecture is not merely qualitative. It asserts that non-entangling dynamics impose channel degeneracies, and those degeneracies are then interpreted as enhanced emergent symmetries. The general logic is: decompose the $S$3-matrix into irreducible channels, require it to be proportional to $S$4 or SWAP, infer equalities among phase shifts, and interpret channel-independence as enlarged invariance (Hu et al., 30 Jul 2025).

Earlier work established the same principle in the spin-$S$5 baryon sector. There the $S$6-wave spin-space $S$7-matrix depends on singlet and triplet phase shifts $S$8, and the entanglement power is

$S$9

Its minima occur when

$$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$0

which coincide with enhanced-symmetry loci of the low-energy EFT, including the Wigner $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$1 line $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$2 and conformal fixed points (Beane et al., 2018).

3. Symmetry enhancement in concrete systems

In the two-flavor nucleon system, entanglement suppression was proposed as an infrared organizing principle for approximate Wigner $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$3 symmetry. In the three-flavor octet-baryon system, the same logic was argued to favor a still larger symmetry, $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$4, in the exact $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$5 limit. The central claim was that dynamical entanglement suppression in infrared strong interactions gives rise to these emergent symmetries and constrains nuclear and hypernuclear forces in dense matter (Beane et al., 2018).

The arbitrary-spin generalization was developed in the study of low-energy scattering of the spin-$$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$6 decuplet baryons. These baryons form the $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$7 of SU(3) flavor and, in spin space, are four-dimensional qudits. When spin and flavor are treated simultaneously with Fermi statistics, the full $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$8-matrix contains eight independent phase shifts. Requiring non-entangling dynamics in spin space imposes explicit equalities among these phases. If all eight become equal, the interaction becomes blind to the full $$|\psi_{\rm in}\rangle = |\psi_A\rangle\otimes |\psi_B\rangle,$$9 spin-flavor index and an emergent

$$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$0

symmetry appears. If instead the $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$1-matrix is proportional to SWAP in spin space, the system realizes

$$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$2

together with nonrelativistic conformal symmetry (Hu et al., 30 Jul 2025).

The same paper applied the conjecture to low-energy heavy-meson scattering in the coupled $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$3-wave channels $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$4 and $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$5. There, heavy-quark spin symmetry already relates the relevant couplings. Imposing entanglement suppression on both scattering matrices and using the observed near-threshold $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$6 as input via

$$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$7

produces two solutions: either all five relevant phase shifts are $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$8, or all isoscalar phases are $$|\psi_{\rm out}\rangle = \hat S\,|\psi_{\rm in}\rangle.$$9 and all isovector phases are zero. In both cases the interaction becomes independent of total angular momentum, which is identified with the light-quark spin symmetry proposed earlier by Voloshin. A stated phenomenological consequence is the prediction of additional near-threshold molecular states, including isovector partners of $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$0 (Hu et al., 30 Jul 2025).

The conjecture has also been probed in systems where the evidence is more tentative. In hyperon-nucleon scattering in the $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$1 sector, global fits of phase shifts were found to give hints of spin-entanglement suppression in most channels, though the $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$2 channel remains inconclusive because NSC97 and ESC16/$\rho_A=\operatorname{Tr}_B\rho_{\rm out}$3EFT fits imply qualitatively different triplet interactions. The paper accordingly proposed recoil and target polarization observables in $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$4 scattering as “quantum” diagnostics to resolve the ambiguity (Liu et al., 2023).

Beyond hadron physics narrowly defined, an analogous argument has been developed in the two-Higgs-doublet model. Treating $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$5 as a two-qubit scattering problem in flavor space, demanding suppression of flavor entanglement forces the broken-phase perturbative $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$6-matrix into the local-equivalence class of the Identity gate. The resulting scalar potential has maximally enhanced

$\rho_A=\operatorname{Tr}_B\rho_{\rm out}$7

symmetry acting on the eight real scalar components, and this in turn implies the alignment limit with a Standard-Model-like Higgs boson (Carena et al., 2023). This suggests that the conjecture can function as a selector of enhanced-symmetry regions of parameter space outside QCD.

4. Identical particles, higher spin, and restricted Hilbert spaces

A major refinement arises for identical particles. In spin-$\rho_A=\operatorname{Tr}_B\rho_{\rm out}$8 baryon scattering, exact vanishing of the naive entanglement power is generally impossible once Fermi-Dirac statistics are imposed, because the physical two-body Hilbert space is not the full tensor product but the symmetry-restricted subspace allowed by exchange antisymmetry. This led to a modified definition of entanglement power in which one averages only over the states surviving the projection $\rho_A=\operatorname{Tr}_B\rho_{\rm out}$9 onto the antisymmetric sector, with normalized post-projection density matrix

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$0

The resulting weighted entanglement power is

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$1

For $$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$2, this becomes especially simple and is used as the main diagnostic (Hu et al., 10 Jun 2025).

The $$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$3 channel is the model example. Because only the flavor-symmetric $$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$4 occurs, only the spin-antisymmetric channels $$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$5 survive. The projected $$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$6-matrix is

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$7

and the modified entanglement power is

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$8

It never vanishes, but it is minimized when

$$S_{\rm vN}(\rho_A)=-\operatorname{Tr}(\rho_A\ln \rho_A)$$9

These minima are interpreted as Identity and SWAP acting on the restricted antisymmetric Hilbert space: $S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$0 while the $S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$1-separated point gives a projected SWAP operator $S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$2 with

$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$3

This suggests that for identical particles the conjecture should be reformulated in terms of global or local minima on the symmetry-allowed subspace, rather than exact zero of the full-space entanglement power (Hu et al., 10 Jun 2025).

The same work proposed a broader spin-$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$4 pattern. For identical spin-$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$5 particles, when the $S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$6-matrix acts as Identity on the allowed sector, the enhanced symmetry is

$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$7

For spin-$S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$8, this gives $S_L(\rho_A)=1-\operatorname{Tr}\rho_A^2.$9 in the statistics-restricted problem. A plausible implication is that the entanglement-suppression principle is robust under increases in local Hilbert-space dimension, but only after the physical Hilbert space is defined consistently with quantum statistics.

5. Alternative formulations beyond hadron scattering

Outside hadronic scattering, the phrase has been used for several technically distinct phenomena. In noisy quantum circuits, “scrambling-induced entanglement suppression” denotes a regime in a 7-qubit teleportation architecture with local dephasing where increasing scrambling strength $S$0 decreases the final logarithmic negativity across the central cut instead of increasing it. The paper identifies a crossover near

$S$1

below which scrambling enhances entanglement and above which it suppresses it. The proposed mechanism is that under strong dephasing, the Bell measurement consumes more entanglement than the scrambling unitary can create (Haas et al., 2024).

In nonlinear modifications of quantum mechanics, entanglement suppression has been proposed as a collapse mechanism. The modified Schrödinger equation

$S$2

acts only on entangled bipartite pure states and vanishes on product states. In the exactly solvable $S$3 case, subsystem purity

$S$4

increases monotonically,

$S$5

so generic states asymptotically approach product branches. The authors interpret this as “spontaneous collapse by entanglement suppression,” with added phenomenological noise supplying stochastic outcome statistics (Buks, 2023).

In quantum information and complexity theory, the problem is reversed: one asks whether a channel can efficiently break entanglement. A dimension-independent channel was recently constructed that maps bipartite unentangled inputs $S$6 to outputs close to mixtures of tensor powers,

$S$7

but only under the promise that the input is already separable across a designated bipartition (Jeronimo et al., 2024). Complementarily, for the subclass of strong disentanglers, it has been proved that any such channel requires exponentially large input dimension when

$S$8

so that

$S$9

as $1$0 (Akibue et al., 2024). This suggests that efficient, universal entanglement suppression is strongly constrained unless the input already has special structure.

Topological and holographic variants shift attention from dynamical minimization to structural constraint. In $1$1 Chern–Simons theory, it has been conjectured that if the link state factorizes across a bipartition for all colorings, then the corresponding sublinks are unlinked; the implication is exact factorization rather than quantitative smallness of entanglement (Chun et al., 2017). In a later TQFT-oriented program, genuine $1$2-partite long-range entanglement of gapped phases was conjecturally related to TQFT partition functions on closed $1$3-manifolds, with verification for general $1$4-dimensional Levin–Wen string-net models (Zotto et al., 18 Feb 2026). In holographic mixed-state dynamics, a proposal paper argues that local-operator entanglement growth may be suppressed in thermal backgrounds, with saturation near scrambling time

$1$5

and interprets the phenomenon through black-hole scattering, OTOCs, and possibly negativity (Momeni, 12 Sep 2025).

6. Critiques, counterexamples, and present status

The conjecture remains heterogeneous and partially controversial. In hadron physics, it is explicitly described as a conjecture, not a theorem of QCD. The arguments are formulated in the low-energy, nonrelativistic, usually $1$6-wave regime, and the resulting symmetries are therefore emergent and approximate rather than exact microscopic symmetries. The spin-$1$7 baryon analysis assumes the SU(3)-symmetric decuplet picture and imposes channel constraints globally, while the heavy-meson application additionally assumes heavy-quark spin symmetry, a near-threshold interpretation of $1$8, and negligible higher partial waves (Hu et al., 30 Jul 2025).

More strongly, some broad “suppression” theses have been explicitly falsified in other branches of quantum information theory. The Peres conjecture, which effectively asserted that PPT or undistillable entanglement is too suppressed to produce Bell nonlocality, was disproved by a bipartite two-qutrit PPT bound-entangled state that violates a Bell inequality (Vértesi et al., 2014). Likewise, the “mostly-bipartite” conjecture for holographic CFT states was argued to be incompatible with standard entanglement-wedge-cross-section dualities: if $1$9 or $S$00, then holographic states must contain $S$01 tripartite entanglement rather than only subleading multipartite structure (Akers et al., 2019). These results do not refute the hadronic conjecture, but they show that strong universal claims of entanglement suppression must be sharply specified.

The present evidentiary status is therefore mixed. The hadronic conjecture has its clearest support where minimal entanglement conditions can be translated into explicit phase-shift degeneracies and then into enhanced symmetries: two-flavor nucleons, three-flavor octet baryons, spin-$S$02 decuplet systems, and heavy mesons (Beane et al., 2018). It is sharpened by the arbitrary-spin and arbitrary-representation framework of recent work (Hu et al., 30 Jul 2025). Yet decisive tests still require external input. The most direct ones proposed are lattice-QCD or experimental determinations of decuplet-baryon phase shifts, searches for additional $S$03 near-threshold states related to $S$04, and polarization measurements in $S$05 scattering that could discriminate among competing phase-shift fits (Liu et al., 2023).

A plausible synthesis is that the Entanglement-Suppression Conjecture is strongest when formulated narrowly: specific dynamics, specific Hilbert-space factorization, and a precise entanglement diagnostic. In that form it functions as a symmetry principle, a classifier of restricted dynamics, or a no-go statement about disentangling resources. In broader or universal form, it remains speculative and, in some contexts, demonstrably false.