Stevens Innovation Expo

1. Preserving Entanglement via Quantum Error CorrectionXinyu Zhao, Samuel R. Hedemann, and Ting YuCenter for Controlled Quantum Systems and the Department of Physics and Engineering Physics,Stevens Institute of Technology, Hoboken, New Jersey 07030, USA Stevens Innovation Expo 1 4 Introduction Quantum coherence and quantum entanglement will deteriorate when the system is coupled to its environment. In this project, we propose a new error-correction scheme based on the random unitary (RU) decomposition of the quantum channel. We show that quantum coherence and entanglement can be recovered by measuring the environment. • 2-qubit common bath • Hamiltonian: , • Non-RU decomposition: • Entanglement restoration: • Unknown initially entangled state: • Using the corresponding restoration operations: • The initial state can be fully recovered as • RU decomposition: • Measurement basis: • Starting from a known set of basis (Fock basis) • The measurement basis for can be constructed by unitary transformation. • can be treated as zero approximately. (see Fig. 2) • Our project: Environmental assisted quantum error correction and entanglement preservation • Advantages of our scheme: • Deterministic process, (ideally 100% successful probability). • High fidelity (ideally, the fidelity is 1). • No extra quantum resources needed. • Restoration operations are unitary. 2 • 1-qubit dephasingbath • Hamiltonian: • Two types of Kraus operators: • If m is odd • If m is even • RU decomposition: Fig. 2 Arbitrary initial state can be fully recovered. Error correction procedure N-qubit common bath – RU decomposition Randomly choose basis, like The RU-type Kraus operators can be chosen as: According to the relation, we can determine the coefficients . 5 Total evolved state System initial state Dephasing channel Env. initial state vacuum Measure the parity of photon numbers Parity is odd or even? Measurement outcome 6 • Conclusion • RU decompositions for N-qubit systems are explicitly constructed. • Quantum coherence and entanglement can be recovered by measuring Fock basis and performing a unitary operation. • Experimental realizations can be made with the existing technologies. Fig. 1 Merits of our scheme: High fidelity (ideally 1), high successful probability (ideally 100%), unitary restoration operation. even odd Final state System collapse into 3 N-qubit separable baths Kraus operators are the tensor products of single qubitsbu-systems. Acknowledgement We acknowledge the grant support  from the NSF PHY-0925174 andthe AFOSR No. FA9550-12-1-0001. System collapse into Restoration where are the Kraus operators for the total system in the case of separable baths, are the Kraus operators of the sub system. References • Xinyu Zhao, Samuel R. Hedemann, and Ting Yu, to be submitted. • M.Gregoratti and R. F. Werner, J. Mod. Opt. 50, 915 (2003).