Bidirectional teleportation using scrambling dynamics: a practical protocol

Abstract

We show that quantum information scrambling can enable a generic SWAP gate between collective degrees of freedom in systems without universal local control. Our protocol combines the Hayden-Preskill recovery scheme, associated with the black hole information paradox, with quantum teleportation and runs them in parallel and in opposite directions, enabling bidirectional exchange of quantum states through global interactions alone. This approach cleanly distinguishes the roles of information spreading, entanglement, and chaos for enabling both coherent state transfer and recovery. We propose an experimental realization using the Dicke model, which can be realized in cavity-QED and trapped-ion platforms, highlighting the utility of holography in designing practical quantum gates.

Figures (4)

• Figure 1: Bidirectional teleportation enabled by scrambling. (a) The full protocol with 3 systems $A,B,C$, with $d_A=d_C$. Systems $A$ and $C$ start in $\rho_{A,\mathrm{in}}$ and $\rho_{C,\mathrm{in}}$, while $B$ is prepared in $|\phi\rangle_B$. A scrambling unitary $U_{AB}$ spreads information in $A$ into $AB$ entangling them. Applying $U^\dagger_{CB}$ and postselecting $B$ onto $|\phi\rangle_B$ heralds success, yielding $\rho_{A,\mathrm{out}}=\rho_{C,\mathrm{in}}$ and $\rho_{C,\mathrm{out}}=\rho_{A,\mathrm{in}}$ with probability $p\sim 1/d_A^2$. (b) Black hole analogue ($A \to C$): recovery from Hawking radiation via decoding, implemented here by reverse evolution and postselection on $B$. (c) Standard quantum teleportation ($C \to A$): $U_{AB}$ supplies an entangled resource and the measurement on $B$ acts as an effective Bell projection given the $A \to C$ mechanism succeeds, teleporting information $C$ to $A$.
• Figure 2: Protocol performance in the Dicke model with $N = 4$ and $\phi = 30$, for $30$ pure initial states in $A$ that are uniformly (Haar) sampled from the Hilbert space SupplementalMaterial. (a) Dependence of fidelity $\mathcal{F}$ on the parameters $\delta/g$ and $\omega_z/g$, averaged over initial states and over times $700\leq gt \leq 850$ (chosen within a regime in which $\mathcal{F}$ remains close to a steady value). (b) Entanglement between $A$ and $B$ quantified by the normalized second Rényi entropy HorodeckiEntanglementReview$S_2(A)\equiv -\log_{d_A}\overline{\mathop{\mathrm{Tr}}\nolimits_A(\rho_A^2)}$ with $d_A=N+1$, where $\overline{\mathop{\mathrm{Tr}}\nolimits_A(\rho_A^2)}$ is the purity in $A$ averaged over initial states over the same time interval; regions of large $\mathcal{F}$ in (a) are seen to correlate with large $S_2$. (c) $\mathcal{F}$ as a function of $gt$ in $A$ at $\delta/g=0.267$ and $\omega_z/g=3.20$, corresponding to maximal $\mathcal{F}$ in (a), showing the attainment of a steady regime of large $\mathcal{F} \sim 0.94$ (inset: the time interval used for averaging in (a)); fluctuations in $\mathcal{F}$ between initial states of up to one standard deviation and non-negative values are shaded. (d) $\mathcal{F}$ vs. $t$ prior to the steady state regime, showing transient regions of acceptable fidelity $\mathcal{F} \geq 0.9$, for the parameters $\delta/g = 0.40$ and $\omega_z/g = 3.78$ corresponding to the earliest such time $gt^\ast = 16.79$ (depicted in Fig. \ref{['fig:transients']} by a red star in Appendix B).
• Figure 3: Early-time operating point distribution with state averaged fidelity above the target value of $0.9$, taken over 30 uniformly chosen (Haar random) initial states in $A$. The figure depicts the threshold time $gt^\ast$ (color-coded) versus $\delta/g$ and $\omega_z/g$, keeping only parameter regions at which $\mathcal{F}(gt^*)\geq 0.9$. The red star marks the target operating point of Fig. \ref{['fig:fourpanel']}d, chosen so that above-threshold fidelity is sustained for three consecutive data points in time ($gt^\ast$ and two successive points each separated by $g\cdot \delta t = 0.15$), embedded in a broad robust region of above-threshold fidelity.
• Figure 4: Reversal imperfections parameterized by fractional mismatches $\epsilon_\delta/\delta$ and $\epsilon_z/\omega_z$. Top row: early-time operating point with parameters as in Fig. \ref{['fig:fourpanel']}d. Bottom row: late-time operating point that maximizes the long-time fidelity with the same parameters as Fig. \ref{['fig:fourpanel']}c. While the early-time regime retains a broad high-fidelity region, the late-time dynamics is markedly more sensitive, with a much narrower tolerance to reversal errors by a relative factor of about $10^{-2}$ compared to the early-time operating point.