Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels

We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than $P$ in a Heisenberg chain of $N$ spin-$\frac{1}{2}$ particles can be achieved in a timescale of the order of $(0.33\hslash ∕J)N^{1.7}\mid \ln P\mid$. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.

Figure 1

Quantum circuit representation of conclusive and arbitrarily perfect state transfer. The first gate at Alice’s qubits represents a NOT gate applied to the second qubit controlled by the first qubit being zero. The qubits ${\mid \mathbf{\psi }⟩}_1^{\left(1\right)}$ on the left-hand side represents an arbitrary input state at Alice’s site, and the qubit ${\mid \mathbf{\psi }⟩}_N^{\left(1\right)}$ represents the same state, successfully transferred to Bob’s site. The ${\tau }_i$ gate represents the unitary evolution of the spin chains for a time interval of ${\tau }_i$.

Figure 2

Semilogarithmic plot of the joint probability of failure $P\left(l\right)$ as a function of the number of measurements $l$. Shown are Heisenberg spin-$\frac{1}{2}$-chains with different lengths $N$. The times between measurements ${\tau }_i$ have been optimized numerically.

Figure 3

Time $t$ needed to transfer a state with a given joint probability of failure $P$ across a chain of length $N$. The points denote exact numerical data, and the fit is given by Eq. (18).

Figure 4

The minimal joint probability of failure $P\left(l\right)$ for chains with length $N$ in the presence of amplitude damping. The parameter $J∕\Gamma$ of the curves is the coupling of the chain (in kelvins) divided by the decay rate $\left(n{s}^{-1}\right)$.