Measurement-induced dynamics for spin-chain quantum communication and its application for optical lattices

We present a protocol for quantum state transfer and remote state preparation across spin chains which operate in their antiferromagnetic mode. The proposed mechanism harnesses the inherent entanglement of the ground state of the strongly correlated many-body systems which naturally exists for free. The uniform Hamiltonian of the system does not need any engineering and, during the whole process, remains intact while a single-qubit measurement followed by a single-qubit rotation are employed for both encoding and inducing dynamics in the system. This, in fact, has been inspired by recent progress in observing spin waves in optical lattice experiments, in which manipulation of the Hamiltonian is hard and instead local rotations and measurements have become viable. The attainable average fidelity stays above the classical threshold for chains up to length 50 and the system shows very good robustness against various sources of imperfection.

Figure 1

(a) Arrays of interacting qubits for which the interaction type is Heisenberg with the exchange coupling $J$. A local control is available for the first qubit to operate a quantum gate or perform a spin measurement. (b) A Bell measurement on the first qubits of two noninteracting chains (note that labeling of the atoms are reversed in each chain) is used for entanglement distribution along the two spin chains.

Figure 2

(a) Two fidelities $F_u^{+}\left(t\right)$ and $F_u^{-}\left(t\right)$ in terms of $Jt$ in a chain of length $N=20$ for the unrestricted measurement protocol. (b) The maximal fidelity $F_{\max }^{+}$ as a function of $N$. (c) The maximal fidelity $F_{\max }^{-}$ as a function of $N$. (d) The optimal time $J{t}_{\mathrm{opt}}$ versus length $N$.

Figure 3

(a) Average fidelity $F_{\mathrm{av}}\left(t\right)$ as a function of $Jt$ for a chain of length $N=20$ in a restricted basis protocol. (b) The maximal average fidelity $F_{\mathrm{av}}\left(t_{\mathrm{opt}}\right)$ in terms of length $N$.

Figure 4

(a) Entanglement $E\left(t\right)$ as a function of $Jt$ for a chain of length $N=40$ (i.e., $N_L=N_R=20)$. (b) The maximal entanglement $E_{\max }$ versus length $N$.

Figure 5

Imperfection effects over a chain of length $N=10$: (a) the fidelity $F_{\max }$ as a function of dimensionless temperature $K_{B}T/J$. Thanks to the SU(2) symmetry of the thermal initial state, all projection bases give the same fidelity. (b) The fidelity $F_{\max }$ as a function of decoherence coupling $\gamma /J$ when the first qubit is projected into $|+\rangle$. (c) The fidelity $\langle F\left(t_{\mathrm{opt}}\right)\rangle$, averaged over 100 different realizations, in terms of randomness strength $\epsilon$ when the first qubit is projected into $|+\rangle$.

Figure 6

(a) Cold atoms in an optical lattice prepared in a Mott insulator phase with exactly one atom per site realizes the Heisenberg Hamiltonian of Eq. (1). A local focused laser beam is used to manipulate the first qubit for both the gate operation and spin measurement. (b) The single-qubit measurement is accomplished by a perpendicular focused laser beam which applies a strong radiation pressure to the state $|\downarrow \rangle$ and leaves the atom unaffected if its quantum state is $|\uparrow \rangle$. (c) Two parallel arrays in a two-dimensional optical lattice are used for entanglement distribution in which a Bell measurement is needed. (d) Bell measurement is fulfilled by tilting the optical lattice such that the singlets tend to occupy a single site and triple pairs remain separated.