Parrondo-type enhancement of quantum-state transfer in spin chains

Abstract

Spin chains have been widely studied as quantum channels for short-distance communication in quantum devices, where many-body dynamics can mediate quantum-state transfer between distant sites. In finite unmodulated chains, however, dispersion and interference effects associated with the static Hamiltonian often limit the achievable transfer fidelity. Here we investigate the transfer of single-qubit and Bell states in finite $XX$ spin chains under periodic switching between two Hamiltonians with different boundary couplings. Inspired by Parrondo's paradox, we examine whether alternating between two configurations that individually yield suboptimal transfer fidelities can generate enhanced coherent transmission. Using Floquet theory together with numerical simulations in the single-excitation subspace, we show that periodic driving can outperform static configurations and achieve higher transfer fidelities. This enhancement originates from the noncommutativity of the driven Hamiltonians and reflects a purely coherent interference effect. We further analyze the dependence of the protocol on system size and driving parameters and examine its robustness to asymmetric boundary couplings. Our results show that the transfer fidelity remains stable under moderate disorder, indicating that simple time-dependent control of boundary couplings provides an effective strategy to enhance quantum-state transfer in spin-chain communication channels and optimize quantum information processing in engineered many-body systems.

Figures (5)

• Figure 1: (Color online) Schematic spin chain with end blocks coupled to a uniform channel. (a) Alice transmits a single-qubit to Bob coupled to a channel with boundary couplings $\alpha$ and near-boundary couplings $\beta$. (b) Alice transmits a two-qubit state coupled by $\alpha$ to Bob with boundary couplings $\beta$. The spin channel couplings are $\gamma=1$.
• Figure 2: Ratio $F/F_0$ obtained at the first arrival transmission peak when Alice sends the state $\ket{1}$ to Bob through a chain with $N=10$ qubits. Here $F$ denotes the maximum fidelity for a given coupling constant $\alpha$, while $F_0$ corresponds to the reference case $\alpha_0=1$, for which $F_0=0.804$. The dashed line indicates the boundary between winning (above the line) and losing (below the line) transmission evolutions. The markers highlight two losing examples given by $\alpha_1=0.50$ and $\alpha_2=1.50$, and a winning case with $\alpha_{\mathrm{max}}=0.73$, which yields the maximum fidelity within this parameter range.
• Figure 3: (a) Maximum fidelity $F$ at the first transmission peak when Alice sends the state $\ket{1}$ from site $1$ to Bob at site $N$, as a function of the Parrondo driving frequency $\omega$ for a chain with $N=10$ qubits. The blue and orange curves correspond to evolutions starting with the losing Hamiltonians $\mathcal{H}_1(0.5)$ and $\mathcal{H}_2(1.5)$, respectively. The dashed line indicates the maximum fidelity obtained in the static uniform case $\alpha_0=1$. (b) Comparison of the transmission fidelity for the individual Hamiltonians and the periodically driven protocol, showing that the Parrondo protocol (red curve) outperforms both static losing strategies.
• Figure 4: Ratio $F/F_0$ at the first transmission peak obtained when Alice sends the Bell state $\ket{\psi^\pm}$ to Bob as a function of the coupling parameter $\beta$ for a chain with $N=10$ qubits. Here $F$ denotes the maximum fidelity for a given $\beta$, while $F_0=0.730$ corresponds to the reference value obtained for $\beta_0=1$. For $\beta<0.40$ the system enters a regime of almost perfect transmission earlier investigated Apo19, which is not considered here since the objective is to improve transmission using individually losing parameters as $\beta_1$, $\beta_2$, and $\beta_3$ above.
• Figure 5: Robustness of the transmission fidelity under asymmetric boundary couplings. (a) Variation of the parameter $\delta\alpha$ for the transfer of the state $\ket{\psi(0)}=\ket{1}$ in a chain with $N=12$ qubits. The parameters are $\beta=1$, $\alpha_1=0.47$, $\alpha_2=1.01$, $\omega=1.84$, and $\eta=0.64$. The disorder parameter $\delta\alpha$ varies from $-0.2$ to $0.2$ with increments of $0.01$. The dashed line indicates the ideal symmetric case ($\delta\alpha=0$). (b) Analogous case for Bell-state transfer $\ket{\psi(0)}=\ket{\psi^+}$, using parameters $\alpha=1$, $\beta_1=0.80$, $\beta_2=1.06$, $\omega=1.78$, and $\eta=0.43$. The disorder parameter $\delta\beta$ follows the same range as $\delta\alpha$. Time evolutions of the transmission fidelities of (c) $\ket{\psi(0)}=\ket{1}$ and (d) $\ket{\psi(0)}=\ket{\psi^+}$ for representative values of $(\delta\alpha,\delta\beta)$ as functions of $\tau$.