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Nature Communications

Portraying entanglement between molecular qubits with four-dimensional inelastic neutron scattering

Elena Garlatti, T. Guidi, Simon Ansbro, Paolo Maria Santini, G. Amoretti, Jacques Ollivier, H. Mutka, Grigore A. Timco, Íñigo J. Vitórica‐Yrezábal, George F. S. Whitehead, Richard E. P. Winpenny, Stefano Carretta

Published Feb 20, 2017• 58 citations
Publisher

Abstract

Abstract Entanglement is a crucial resource for quantum information processing and its detection and quantification is of paramount importance in many areas of current research. Weakly coupled molecular nanomagnets provide an ideal test bed for investigating entanglement between complex spin systems. However, entanglement in these systems has only been experimentally demonstrated rather indirectly by macroscopic techniques or by fitting trial model Hamiltonians to experimental data. Here we show that four-dimensional inelastic neutron scattering enables us to portray entanglement in weakly coupled molecular qubits and to quantify it. We exploit a prototype (Cr7Ni)2 supramolecular dimer as a benchmark to demonstrate the potential of this approach, which allows one to extract the concurrence in eigenstates of a dimer of molecular qubits without diagonalizing its full Hamiltonian.

DOI
10.1038/ncomms14543

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Abstract Entanglement is a crucial resource for quantum information processing and its detection and quantification is of paramount importance in many areas of current research. Weakly coupled molecular nanomagnets provide an ideal test bed for investigating entanglement between complex spin systems. However, entanglement in these systems has only been experimentally demonstrated rather indirectly by macroscopic techniques or by fitting trial model Hamiltonians to experimental data. Here we show that four-dimensional inelastic neutron scattering enables us to portray entanglement in weakly coupled molecular qubits and to quantify it. We exploit a prototype (Cr7Ni)2 supramolecular dimer as a benchmark to demonstrate the potential of this approach, which allows one to extract the concurrence in eigenstates of a dimer of molecular qubits without diagonalizing its full Hamiltonian.
Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, which are now made selectively available by four-dimensional inelastic neutron scattering.
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Measuring quantum entanglement in solid state systems has been a long-standing challenge. Here, the authors use three entanglement witnesses borrowed from quantum information theory to directly detect quantum entanglement in the 1D Heisenberg spin chain system KCuF3{}_{3}3​ using inelastic neutron scattering data. The results are validated using density matrix renormalization group calculations and show that model-independent measures of quantum spin entanglement are experimentally possible, as well as reveal which witnesses are more experimentally robust.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
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We show that molecular nanomagnets provide an ideal platform to investigate entanglement in qubit-qudit and qudit-qudit pairs. A prototypical example is Yb 173 (trensal), embedding an electronic spin qubit coupled to a nuclear spin qudit. We demonstrate violation of generalized Bell inequalities on this molecule by developing an optimized pulse sequence and by performing realistic numerical simulations using experimentally measured Hamiltonian parameters and coherence times. We find that the inequalities are safely violated in a wide range of parameters, proving the robustness of entanglement in the investigated system. Furthermore, we propose a scheme to study qudit-qudit entanglement on a molecular spin trimer, in which two spins 3/2 are linked via an interposed switch to turn on and off their mutual interaction.