Postertitle Author 1, Author 2, Room location Preserving Entanglement via Quantum Error Correction Xinyu Zhao, Samuel R. Hedemann, and Ting Yu Center for Controlled Quantum Systems and the Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA Stevens Innovation Expo 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. 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. Our project: Environmental assisted quantum error correction and entanglement preservation 1-qubit dephasing bath Hamiltonian: Two types of Kraus operators: If m is odd If m is even RU decomposition: System initial state Env. initial state vacuum Total evolved state Dephasing channel Parity is odd or even? Measure the parity of photon numbers Measurement outcome odd System collapse into System collapse into even Final state Restoration Error correction procedure Merits of our scheme: High fidelity (ideally 1), high successful probability (ideally 100%), unitary restoration operation. 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) 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 . 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. References Xinyu Zhao, Samuel R. Hedemann, and Ting Yu, to be submitted. M.Gregoratti and R. F. Werner, J. Mod. Opt. 50, 915 (2003). N-qubit separable baths Kraus operators are the tensor products of single qubit sbu-systems. where are the Kraus operators for the total system in the case of separable baths, are the Kraus operators of the sub system. Fig. 1 Fig. 2 Arbitrary initial state can be fully recovered. Acknowledgement We acknowledge the grant support  from the NSF PHY-0925174 and the AFOSR No. FA9550-12-1-0001. 1 2 3 4 5 6
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Stevens Innovation Expo

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Preserving Entanglement via Quantum Error Correction Xinyu Zhao, Samuel R. Hedemann , and Ting Yu Center 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. - PowerPoint PPT Presentation
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Postertitle Author 1, Author 2, Room location Preserving Entanglement via Quantum Error Correction Xinyu Zhao, Samuel R. Hedemann, and Ting Yu Center for Controlled Quantum Systems and the Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA Stevens Innovation Expo 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. 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. Our project: Environmental assisted quantum error correction and entanglement preservation 1-qubit dephasing bath Hamiltonian: Two types of Kraus operators: If m is odd If m is even RU decomposition: System initial state Env. initial state vacuum Total evolved state Dephasing channel Parity is odd or even? Measure the parity of photon numbers Measurement outcome odd System collapse into System collapse into even Final state Restoration Error correction procedure Merits of our scheme: High fidelity (ideally 1), high successful probability (ideally 100%), unitary restoration operation. 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) 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 . 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. References Xinyu Zhao, Samuel R. Hedemann, and Ting Yu, to be submitted. M.Gregoratti and R. F. Werner, J. Mod. Opt. 50, 915 (2003). N-qubit separable baths Kraus operators are the tensor products of single qubit sbu-systems. where are the Kraus operators for the total system in the case of separable baths, are the Kraus operators of the sub system. Fig. 1 Fig. 2 Arbitrary initial state can be fully recovered. Acknowledgement We acknowledge the grant support  from the NSF PHY-0925174 and the AFOSR No. FA9550-12-1-0001. 1 2 3 4 5 6
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