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arXiv:quant-ph/0610210 · Physical Review A

Quantum state transfer in spin-1 chains

Oriol Romero‐Isart, K. Eckert, Anna Sanpera

Published May 16, 2007• 51 citations
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Abstract

We study the transfer of a quantum state through a Heisenberg spin-1 chain prepared in its ground state. We characterize the efficiency of the transfer via the fidelity of retrieving an arbitrarily prepared state and also via the transfer of quantum entanglement. The Heisenberg spin-1 chain has a very rich quantum phase diagram. We show that the boundaries of the different quantum phases are reflected in sharp variations of the transfer efficiency. In the vicinity of the border between the dimer and the ferromagnetic phase (in the conjectured spin-nematic region), we find strong indications for a qualitative change of the excitation spectrum. Moreover, we identify two regions of the phase diagram that give rise to particularly high transfer efficiency; the channel might be nonclassical even for chains of arbitrary length, in contrast to spin-$1∕2$ chains.

DOI
10.1103/physreva.75.050303

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We study the transfer of a quantum state through a Heisenberg spin-1 chain prepared in its ground state. We characterize the efficiency of the transfer via the fidelity of retrieving an arbitrarily prepared state and also via the transfer of quantum entanglement. The Heisenberg spin-1 chain has a very rich quantum phase diagram. We show that the boundaries of the different quantum phases are reflected in sharp variations of the transfer efficiency. In the vicinity of the border between the dimer and the ferromagnetic phase (in the conjectured spin-nematic region), we find strong indications for a qualitative change of the excitation spectrum. Moreover, we identify two regions of the phase diagram that give rise to particularly high transfer efficiency; the channel might be nonclassical even for chains of arbitrary length, in contrast to spin-1∕21∕21∕2 chains.
Quantum communication protocols based on spin chains have been extensively studied, yet their ability to transmit nonstabilizer resources has not been systematically addressed. We investigate the transport of quantum magic in spin chains through the natural dynamics of systems initialized in nonstabilizer states, and quantify the transported resource via the stabilizer norm. We analyze three experimentally feasible state-transfer protocols, ranging from noisy to (quasi-)perfect transfer, including one realizable in trapped-ion platforms. We find that the geometry of the injected state strongly influences transport: states in the lower Bloch hemisphere achieve higher transfer quality, whereas states in the upper hemisphere give rise to an efficient magic transport only beyond a threshold value of the parameter controlling the tendency towards perfect transfer. These features are robust across all protocols and identify the Hamiltonian and state properties that favor high-quality transfer. Moreover, we identify a parameter region, relevant to the initial state preparation, in which the transported magic exceeds the initial encoding, indicating that such spin systems can act as magic-amplification channels. Our results establish the conditions for efficient transport of nonstabilizer resources and demonstrate quantum magic as a sensitive probe of quantum transport beyond population dynamics.
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