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 |
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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
Brachistochrone of entanglement for spin chains. / Carlini, Alberto; Koike, Tatsuhiko.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 10, 105304, 08.02.2017.Research output: Contribution to journal › Article
}
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 -