### Abstract

We analytically investigate the role of entanglement in time-optimal state evolution as an application of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly coupled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for W and Greenberger-Horne-Zeilinger (GHz) initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.

Original language | English |
---|---|

Article number | 105304 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 50 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2017 Feb 8 |

### Fingerprint

### Keywords

- entanglement
- Ising chain
- optimal quantum control

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*50*(10), [105304]. https://doi.org/10.1088/1751-8121/aa59df

**Brachistochrone of entanglement for spin chains.** / Carlini, Alberto; Koike, Tatsuhiko.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 50, no. 10, 105304. https://doi.org/10.1088/1751-8121/aa59df

}

TY - JOUR

T1 - Brachistochrone of entanglement for spin chains

AU - Carlini, Alberto

AU - Koike, Tatsuhiko

PY - 2017/2/8

Y1 - 2017/2/8

N2 - We analytically investigate the role of entanglement in time-optimal state evolution as an application of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly coupled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for W and Greenberger-Horne-Zeilinger (GHz) initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.

AB - We analytically investigate the role of entanglement in time-optimal state evolution as an application of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly coupled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for W and Greenberger-Horne-Zeilinger (GHz) initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.

KW - entanglement

KW - Ising chain

KW - optimal quantum control

UR - http://www.scopus.com/inward/record.url?scp=85013059708&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013059708&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aa59df

DO - 10.1088/1751-8121/aa59df

M3 - Article

AN - SCOPUS:85013059708

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

M1 - 105304

ER -