Traversable Wormhole Protocol

• Traversable wormhole protocol is a mechanism that couples two entangled quantum systems via a double-trace deformation to generate negative null energy, enabling signals to traverse previously inaccessible regions.
• The protocol’s methods are demonstrated in nearly-AdS₂ settings, SYK models, and higher-dimensional holographic frameworks, providing equivalent descriptions as geometric shockwaves, teleportation circuits, and noisy quantum channels.
• Practical implications include quantifying quantum channel capacity, understanding probe dependence in signal transmission, and informing experimental implementations for quantum information and gravitational studies.

Traversable wormhole protocol denotes a class of procedures in which two highly entangled quantum systems—most often the two sides of a thermofield-double state dual to an eternal black hole—are coupled so that a signal inserted on one side can emerge on the other. In bulk language, the coupling generates negative null energy, a shockwave, or an equivalent horizon shift that opens a causal channel; in boundary language, the same process appears as a teleportation protocol, a nonlocal double-trace deformation, or a quantum channel with finite capacity. The same phrase is also used more broadly for constructive recipes that make wormhole geometries traversable by localizing exotic matter, modifying the gravitational sector, or introducing geometric defects (Maldacena et al., 2017, Bak et al., 2018, Lu et al., 27 Mar 2026, Garattini, 2019).

1. Canonical architecture of the protocol

A standard formulation begins with a thermofield-double state

$$|\mathrm{TFD}\rangle=\frac{1}{\sqrt{Z}}\sum_n e^{-\beta E_n/2}|E_n\rangle_L|\overline{E}_n\rangle_R,$$

or, in explicit teleportation setups, with a Bell pair carrying the message together with a left-right TFD resource. Information is injected as a simple right- or left-side excitation, the two sides evolve, and a brief coupling is applied between them. In the Gao–Jafferis–Wall-type formulation this coupling is written as

$$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$

with large $K$ used to suppress unwanted particle creation and make the deformation resemble a geometric shockwave (Lu et al., 27 Mar 2026).

In the bulk description, the deformation produces a null shift experienced by the probe. One summary formula is

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$

so the operational question is whether the induced shift is large enough to move the excitation through a region that was previously causally inaccessible. In nearly-$AdS_2$, the same mechanism is encoded in the two-sided correlator

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$

whose nonvanishing commutator signals successful traversal (Maldacena et al., 2017).

This architecture admits several equivalent readings. In semiclassical gravity it is a negative-energy opening of an Einstein–Rosen bridge. In boundary many-body dynamics it is a scrambling-assisted teleportation circuit. In quantum information language it is a noisy bipartite channel between code subspaces. These are not separate protocols so much as distinct descriptions of the same operational sequence.

2. Gravitational mechanism and bulk realization

In the nearly-$AdS_2$/JT setting, the protocol is implemented by a double-trace deformation

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$

added to the two boundaries of an eternal black hole. The metric remains locally $AdS_2$, but the dilaton responds to the induced stress tensor, and the negative null energy shifts the future singularity or horizon so that a signal can traverse. The bulk solution of the teleportation process shows that the horizon radius or entropy changes consistently with the boundary energy shift, satisfying the first law through relations such as

$$\delta S_{BH}=\frac{\bar\phi}{4G}\delta L,\qquad \delta E_R=T\,\delta S.$$

At leading order, the traversability produced by the deformation survives the backreaction of the teleportee itself (Bak et al., 2018).

A complementary nearly-$$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$0 picture emphasizes that gravity reduces to the motion of the UV boundaries in a rigid $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$1 background. The interaction $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$2 acts as an attractive impulse between the two boundary trajectories, pulling them closer so that the future light cone from one side can intersect the other. In the probe limit the effect is a pure null translation,

$$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$3

which is why the teleportee is described as feeling “nothing special” while passing through the wormhole (Maldacena et al., 2017).

Higher-dimensional static realizations preserve the same logic while changing the source of negative energy. An eternal traversable wormhole in asymptotically $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$4 can be obtained by coupling two identical holographic CFTs through a single low-dimension operator. In the bulk, Einstein–Maxwell gravity with a massless charged Dirac fermion and magnetic flux produces a lowest-Landau-level sector whose renormalized stress tensor satisfies

$$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$5

The wormhole is static, eternal, and is argued to be dual to the ground state of a simple coupled Hamiltonian (Bintanja et al., 2021).

The same negative-energy support reappears in asymptotically flat magnetic wormholes. In the Maldacena–Milekhin–Popov geometry studied via scattering, two near-extremal magnetically charged black holes are glued into a long $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$6-like throat, and traversability is provided by negative Casimir energy from fermions in the lowest Landau level. This establishes that the protocol is not restricted to JT kinematics, although the admissible probes and frequencies become far more constrained (Freivogel et al., 10 Jun 2026).

3. Teleportation, scrambling, and SYK realizations

The protocol acquired its most influential interpretation when quantum teleportation was re-read geometrically through ER=EPR. In that formulation, Alice and Bob share an entangled mediator, Alice combines the teleportee with her side, classical data are transmitted, and Bob applies a recovery operation. The crucial claim is that the classical bit string carries no information about the teleported state itself; instead, the teleported system passes through the Einstein–Rosen bridge and can retain a memory of what it encountered inside the wormhole (Susskind et al., 2017).

A fully explicit many-body realization appears in the SYK model. Two SYK systems $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$7 are prepared in the TFD state

$$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$8

a qubit is inserted by a SWAP operation into a left fermionic mode at time $$U=e^{igV},\qquad V(t)=\frac{1}{K}\sum_{i=1}^K O_L^i(-t)O_R^i(t),$$9, the systems evolve, and the interaction

$K$0

is applied at the midpoint. Extraction on the right is again performed by a SWAP. Perfect teleportation corresponds to

$K$1

and an improved encoding into a product of $K$2 Majorana operators gives, for $K$3,

$K$4

which is the paper’s almost-perfect-fidelity regime (Gao et al., 2019).

The same circuit can also operate without a semiclassical gravity interpretation. In “peaked-size teleportation,” the coupling

$K$5

acts approximately as a size-dependent phase on Pauli strings when the operator-size distribution is narrow. The condition

$K$6

ensures that different components acquire nearly the same phase, allowing teleportation in generic thermalizing systems such as random unitary circuits, high-temperature SYK, and one-dimensional spin chains. In this framework late-time one-qubit teleportation is universal, while at intermediate times many-qubit teleportation is possible if operator sizes add, subject to the strict bound

$K$7

The paper distinguishes this generic mechanism from the low-temperature holographic regime, where size winding rather than narrow size distributions is the relevant microscopic structure (Schuster et al., 2021).

A further quantum-information variant replaces measurement-based teleportation by a fully unitary, entanglement-recycling circuit. Using two shared EPR pairs, a three-qubit unitary $K$8, and a single transmitted “middle” qubit, the protocol realizes

$K$9

The exchanged qubit remains maximally mixed,

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$0

which is the basis of the paper’s unconditional-security claim (Czelusta et al., 2021).

4. Quantum-channel formulation and capacity

The traversable wormhole protocol admits a direct quantum-channel description. One formulation defines a bipartite channel

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$1

with input excitations localized in a left code subspace and outputs decoded on the right. Because the full CFT evolution is unitary but the relevant subregions are traced, the induced map is generically non-unitary and noisy. A finite-dimensional approximation is obtained by encoding into a code subspace through a map $$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$2, evolving by the full protocol, and decoding with $$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$3, giving an approximate channel $$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$4 (Bao et al., 2018).

Within this language, successful traversal is both a communication task and a partial entanglement witness. The number of pulses that can be sent before backreaction closes the wormhole gives a lower bound on quantum communication capacity,

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$5

Repeated pulse experiments become a kind of wormhole tomography: they do not certify all entanglement, but they constrain the subset of states compatible with a classical traversable geometry (Bao et al., 2018).

A more recent development computes the genuine quantum channel capacity of the Gao–Jafferis–Wall protocol. Under the additivity assumption, the channel capacity reduces to coherent information and is governed by the derivative of an out-of-time-ordered correlator: $$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$6 The boost expectation value controlling this capacity is therefore tied directly to operator-size growth in the dual many-body system. Near scrambling, the capacity grows as

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$7

and the chaos bound gives

$$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$8

so Einstein gravity defines the maximal-growth benchmark (Lu et al., 27 Mar 2026).

Backreaction also limits capacity in explicit geometries. In traversable BTZ wormholes, the negative-energy opening is modeled by an $$a^+\sim p_-G_N\sim -gG_N e^t,\qquad S=e^{i\hat P_+ a^+},$$9-shock and the message by a positive-energy $AdS_2$0-shock. Exact colliding-shell constructions show that transferable information is only $AdS_2$1 bits for most times, and that traversibility decreases in multiple-shock geometries. The same formalism is then used to connect decreasing traversibility to the post-Page regime of black-hole evaporation and to show that the negative-energy shock delays scrambling,

$AdS_2$2

which supports the “fast decoder” interpretation (Hirano et al., 2019).

5. Operational diagnostics and probe dependence

A central experimental and conceptual issue is how one distinguishes genuine bulk traversal from direct boundary signaling. In JT gravity with a double-trace interaction, two channels coexist. The boundary channel is direct and effectively instantaneous from the boundary viewpoint, while the bulk channel respects bulk causality and emerges only after a finite delay. In transitional black-hole-to-eternal-traversable-wormhole geometries, the output frequency is generically modulated, for example

$AdS_2$3

or more generally

$AdS_2$4

Time delay and frequency modulation are therefore proposed as signatures of propagation through the interior rather than through the direct boundary coupling (Bak et al., 2019).

Probe dependence becomes even sharper in four-dimensional magnetic wormholes. For low-frequency scalar probes in the Maldacena–Milekhin–Popov wormhole, the transmission amplitude satisfies

$AdS_2$5

so away from resonances scalar transmission is suppressed as

$AdS_2$6

At early times, most of the wave is reflected or temporarily trapped in the throat; at late times, the accumulated transmission cross-section approaches

$AdS_2$7

where $AdS_2$8 is the horizon area of the corresponding black hole. Resonances at

$AdS_2$9

give perfect scalar transmission with $$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$0 (Freivogel et al., 10 Jun 2026).

Charged massless fermions behave very differently. Because the lowest Landau level removes the centrifugal barrier, the effective reduced dynamics is a massless Dirac channel, and the low-energy transmission is essentially

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$1

The paper relates this to monopole–fermion scattering and the Callan–Rubakov effect. Its practical conclusion is correspondingly asymmetric: scalar probes are best for revealing wormhole structure, while charged massless fermions are the best carriers of information through the wormhole (Freivogel et al., 10 Jun 2026).

These results rule out a common simplification according to which “traversable” means equally transparent to all excitations. The protocol can open a causal passage and still remain highly selective in frequency, spin, charge, or time of observation.

6. Implementations and generalizations

Several generalizations retain the basic logic of negative-energy support while changing the dynamical substrate. On the string worldsheet, an open string in AdS provides a two-sided horizon whose endpoints play the role of asymptotic boundaries. A bilocal endpoint coupling

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$2

creates the required negative null energy on the worldsheet. Unlike the standard Gao–Jafferis–Wall operator $$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$3, the derivative coupling is irrelevant, bends the boundaries inward toward the IR, and makes the effective geometry resemble a cutoff spacetime. In the cutoff analysis, the interval around the optimal traversal time

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$4

widens as the cutoff moves deeper into the bulk, improving transfer efficiency (Boer et al., 2022).

Conservation laws produce another variant. If the two asymptotic boundaries of a black brane are coupled through conserved $$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$5 currents,

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$6

the relevant bulk field is a diffusive Maxwell mode rather than a scalar. The one-loop gauge-field stress tensor can violate ANEC, and the wormhole opening satisfies

$$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$7

However, once the hydrodynamic cutoff is imposed, strong momentum relaxation hinders rather than helps traversability: $$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$8 The resulting many-body teleportation protocol is therefore explicitly diffusion-limited (Ahn et al., 2022).

Hardware realizations have focused on SYK-like circuits shallow enough for NISQ devices. A quantum-processor implementation uses a chaotic binary sparse $$C=\langle e^{-igV}\,\phi_L(t_L)\,e^{igV}\,\phi_R(t_R)\rangle,$$9 SYK model with $AdS_2$0 retained terms, a point that preserves the relevant spectral-chaos diagnostics while reducing circuit depth. The TFD state is prepared variationally to about $AdS_2$1 fidelity using $AdS_2$2 echoed cross-resonance gates; the full circuit uses $AdS_2$3 qubits total; and the final $AdS_2$4 is reconstructed by two-qubit tomography. The diagnostic is the mutual-information asymmetry

$AdS_2$5

whose peak near the expected teleportation time is the robust signature of the traversable sign. The hardware circuits remain deep—about $AdS_2$6 two-qubit gates and depth $AdS_2$7—so the agreement with exact theory is explicitly qualitative rather than quantitative (Byun et al., 11 Apr 2026).

Multi-mouth constructions extend the idea from one causal bridge to a network. Starting from a two-mouth asymptotically flat traversable wormhole supported by negative Casimir energy, a sufficiently small near-extremal black hole can be inserted deep in the throat without destroying traversability provided

$AdS_2$8

Treating the inserted black hole as the mouth of a second wormhole and rendering that new throat traversable yields a geometry through which any pair of mouths can communicate. In the three-mouth case the resulting topology has fundamental group $AdS_2$9, not the $$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$0 that would arise from three independent pairwise wormholes (Emparan et al., 2020).

7. Alternative construction protocols and contested meanings

Outside holographic teleportation, “traversable wormhole protocol” is also used for metric-construction recipes. In standard Morris–Thorne general relativity, one route is to impose an inhomogeneous equation of state $$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$1 with $$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$2, which gives

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$3

Choosing Yukawa-like profiles such as

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$4

or the shifted profile

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$5

localizes the negative energy near the throat. For the first choice, the volume integral quantifier satisfies

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$6

and the shifted profile is described as energetically favored because it produces less negative energy density at the throat. The paper is explicit, however, that this does not eliminate exotic matter; it only localizes it and softens the global bookkeeping (Garattini, 2019).

A more radical claim is made in Unimodular Gravity. There the traceless field equations,

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$7

are combined with a Morris–Thorne ansatz of constant redshift and anisotropic equations of state

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$8

The resulting shape function is

$$\delta H(t)=-h(t)\,\mathcal O_R(t)\mathcal O_L(-t),$$9

and the example $AdS_2$0, $AdS_2$1, $AdS_2$2, $AdS_2$3 is reported to satisfy NEC, WEC, DEC, and SEC according to the paper’s plots. The authors therefore present the construction as a traversable-wormhole recipe without exotic matter (Agrawal et al., 2022).

An even stronger departure from the standard protocol language appears in vacuum-defect wormholes. There the throat is not held open by matter at all, but by a degenerate metric

$AdS_2$4

whose determinant vanishes at $AdS_2$5. For $AdS_2$6, the stress tensor vanishes identically,

$AdS_2$7

and the solution is presented as an exact vacuum wormhole in first-order gravity. The same paper also states that multiple vacuum-defect wormholes appear to allow backward time travel (Klinkhamer, 2023).

Nonperturbative creation protocols push the term in yet another direction. One proposal uses an instanton describing cosmic-string breaking,

$AdS_2$8

to nucleate two massive endpoints with arbitrarily small acceleration, then argues that the endpoints can be replaced by small black holes with identified horizons. Because the mouths can remain essentially at rest rather than rapidly accelerating apart, semiclassical backreaction from quantum fields is then expected to make the resulting wormhole traversable (Horowitz et al., 2019).

This suggests that the phrase now straddles two literatures. In one, it denotes an operational information-transfer scheme implemented by entanglement, scrambling, and an interboundary coupling. In the other, it denotes a constructive set of conditions under which a spacetime geometry itself becomes traversable. The first usage is centered on channel dynamics and teleportation; the second on support conditions, energy conditions, and global geometry.