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International Journal of Theoretical Physics

Generation and Transfer of Quantum Entangled State via Spin-Parity Measurements

Ping Dong, Gang Zhang, Zhuo‐Liang Cao

Published Mar 31, 2010• 0 citations
Publisher
DOI
10.1007/s10773-010-0332-3

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Abstract Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77 , 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.

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Spin qubits in semiconductor quantum dots are a promising candidate for scalable quantum computation. A key step in quantum error correction with spin qubits is the capability to perform high-fidelity parity measurement much faster than the coherence time and to generate entanglement deterministically. Here we propose a parity measurement scheme for two spin qubits by modulated pulses, using a superconducting resonator as a detector. We show that the distinction between spin-parity states can be achieved with a high fidelity within a short measurement time. The combination of parity measurement and feedback control allows the deterministic preparation of various spin entangled states. In addition, the method can be directly applied to parity measurements and surface codes of multiple spin qubits. These results pave the way for fault-tolerant quantum computation with spin qubits.
Recent work has shown that use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity, and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (C. Hill, J. Ralph, Phys. Rev. A 77, 014305 (2008)), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.
Abstract Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. Here we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77 , 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.