Abstract According to holography, entanglement is the building block of spacetime; therefore, drastic changes of entanglement will lead to interesting transitions in the dual spacetime. In this paper, we study the effect of projective measurements on the Sachdev-Ye-Kitaev (SYK) model’s thermofield double state, dual to an eternal black hole in Jackiw-Teitelboim (JT) gravity. We calculate the (Renyi-2) mutual information between the two copies of the SYK model upon projective measurement of a subset of fermions in one copy. We propose a dual JT gravity model that can account for the change of entanglement due to measurement, and observe an entanglement wedge phase transition in the von Neumann entropy. The entanglement wedge for the unmeasured side changes from the region outside the horizon to include the entire time reversal invariant slice of the two-sided geometry as the number of measured Majorana fermions increases. Therefore, after the transition, the bulk information stored in the measured subsystem is not entirely lost upon projection in one copy of the SYK model, but rather teleported to the other copy. We further propose a decoding protocol to elucidate the teleportation interpretation, and connect our analysis to the physics of traversable wormholes.
We study the thermodynamic properties of a two-site coupled complex
q-body Sachdev-Ye-Kitaev (SYK) model in the large-
N limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped, and for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is a good indicator to study the phase diagram of the model; it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with $SL(2,R)\ifmmode\times\else\texttimes\fi{}U(1)$ symmetry with an additional potential and an extra degree of freedom related to the charge. In the large
N and low temperature limit, results from this low energy action are consistent with those from the solution of the SD equations. Likewise, a large-
q analytical calculation of thermodynamic properties confirms the existence of the wormhole phase. Our findings are a preliminary step toward the characterization of traversable wormholes by its field theory dual, a charged strongly interacting fermionic system, that is easier to model experimentally.
We implement the Wormhole-Inspired Teleportation Protocol (WITP) in a pair of coupled Sachdev-Ye-Kitaev (SYK) models prepared in a thermofield-double state, forming a quantum analog of a traversable wormhole. By varying parameters (temperature $\ensuremath{\beta}$, coupling strength
g, insertion site, and traversal time
t) we compare the teleportation fidelity against an analogous protocol using a transverse-field Ising model. We find that the chaotic SYK system consistently yields higher teleportation fidelity than the transverse field Ising model, reflecting the SYK Hamiltonian's pronounced many-body chaos. These enhanced fidelities arise from the SYK's effectively random-matrix dynamics, which improve the coherent information transfer through the wormhole channel. Unlike prior single-qubit benchmarks based on $|0\ensuremath{\rangle}$ inputs, the present work defines and evaluates a genuine quantum-state fidelity for a maximally entangled two-qubit Bell input, using a Pauli-stabilizer formalism that captures entanglement-phase coherence. Our central result is achieved by teleporting a maximally entangled two-qubit Bell state through the wormhole. We introduce a Pauli-stabilizer fidelity measure for the two-qubit message and demonstrate that the Bell-state protocol produces a substantial fidelity boost compared to single-qubit teleportation. Furthermore, we examine the time-resolved fidelity for both single-qubit and two-qubit messages, revealing distinct fluctuation patterns that deepen our understanding of dynamical many-body teleportation processes. Finally, we present an argument that our Bell-state WITP simulations provide a concrete numerical testbed for aspects of the ER = EPR conjecture, by mapping entanglement structure and thermal/coupling dependence to traversability diagnostics in an emergent wormhole geometry.
Abstract In this paper, we study the entanglement entropy between two SYK systems with bilinear coupling. We use the replica trick to calculate the entanglement entropy in the ground state. In parallel, we calculate the entanglement entropy through the Ryu-Takayanagi formula in gravity. For the ground state that is dual to an eternal traversable wormhole in AdS2, the bulk quantum correction to the entanglement entropy is of the same order as the minimal surface area. The ground state of the coupled system is close to a thermofield double state with particular temperature and they have the same entanglement entropy. From the gravity point of view, we explain why the two states have the same entanglement entropy. We also study a case with time-dependent coupling, which involves finding the quantum extremal surface in the bulk.
Abstract We extend the results of arXiv:2209.12903 by studying local projective measurements performed on subregions of two copies of a CFT2 in the thermofield double state and investigating their consequences on the bulk double-sided black hole holographic dual. We focus on CFTs defined on an infinite line and consider measurements of both finite and semi-infinite subregions. In the former case, the connectivity of the bulk spacetime is preserved after the measurement. In the latter case, the measurement of two semi-infinite intervals in one CFT or of one semi-infinite interval in each CFT can destroy the Einstein-Rosen bridge and disconnect the bulk dual spacetime. In particular, we find that a transition between a connected and disconnected phase occurs depending on the relative size of the measured and unmeasured subregions and on the specific Cardy state the measured subregions are projected on. We identify this phase transition as an entangled/disentangled phase transition of the dual CFT system by computing the post-measurement holographic entanglement entropy between the two CFTs. We also find that bulk information encoded in one CFT in the absence of measurement can sometimes be reconstructed from the other CFT when a measurement is performed, or can be erased by the measurement. Finally, we show that a purely CFT calculation of the Renyi entropy using the replica trick yields results compatible with those obtained in our bulk analysis.
Recent work has shown that coupling two identical Sachdev-Ye-Kitaev (SYK) models can realize a phase of matter that is holographically dual to an eternal traversable wormhole.This phase supports revival oscillations between two quantum chaotic systems that can be interpreted as information traversing the wormhole.Here we generalize these ideas to a pair of coupled SYK models with complex fermions that respect a global U(1) charge symmetry.Such models show richer behavior than conventional SYK models with Majorana fermions and may be easier to realize experimentally.We consider two different couplings, namely, tunneling and charge-conserving two-body interactions, and obtain the corresponding phase diagram using a combination of numerical and analytical techniques.At low temperature, we find a charge-neutral gapped phase that supports revival oscillations, with a ground state close to the thermofield double, which we argue is dual to a traversable wormhole.We also find two different gapless non-Fermi liquid phases with tunable charge density which we interpret as dual to a "large" and "small" charged black hole.The gapped and gapless phases are separated by a first-order phase transition of the Hawking-Page type.Finally, we discuss an SU(2)-symmetric limit of our model that is closely related to proposed realizations of SYK physics with spinful fermions in graphene, and explain its relevance for future experiments on this system.