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Chinese Physics Letters

Linear Optical Realization of Qubit Purification with Quantum Amplitude Damping Channel

Lin Qing, Jian Li, Guo Guang-Can

Published Jun 28, 2007• 14 citations
Publisher

Abstract

We provide an experimental scheme which includes the realization of quantum amplitude damping channel and the optimal two-qubit purification. Moreover, we discuss the purification of arbitrary input qubits and arbitrary N qubits. Our scheme only uses linear optical elements and the proposal may be useful in transmission of photons in fibres. This scheme is feasible in the laboratory with the current experimental technology.

DOI
10.1088/0256-307x/24/7/007

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This thesis deals with the implementation of quantum channels using linear optics. We begin with overviews of some important concepts in both quantum information and quantum optics. First, we discuss the quantum bit and describe the evolution of the states via quantum channels. We then discuss both quantum state and process tomography, methods for how to determine which states and operations we are experimentally implementing in the lab. Second, we discuss topics in quantum optics such the generation of single photons, polarization entanglement, and the construction of an entangling gate. \n \nThe first experiment is the implementation of a quantum damping channel, which intentionally can add a specific type and amount of decohering noise to a photonic qubit. Specifically, we realized a class of quantum channels which contains both the amplitude-damping channel and the bit-flip channel, and did so with a single, static, optical setup. Many quantum channels, and some gates, can only be implemented probabilistically when using linear optics and postselection. Our main result is that the optical setup achieves the optimal success probability for each channel. Using a novel ancilla-assisted tomography, we characterize each case of the channel, and find process fideilities of $0.98 \\pm 0.01$ for the amplitude-damping channel and $0.976 \\pm 0.009$ for the bit-flip. \n \nThe second experiment is an implementation of a protocol for quantum computing on encrypted data. The protocol provides the means for a client with very limited quantum power to use a server's quantum computer while maintaining privacy over the data. We perform a quantum process tomography for each gate in a universal set, showing that only when the proper decryption key is used on the output states, which is hidden from the server, then the action of the quantum gate is recovered. Otherwise, the gate acts as the completely depolarizing channel.

•Sep 28, 2012•0 citations
We provide an experimental scheme which includes the realization of quantum amplitude damping channel and the optimal two-qubit purification. Moreover, we discuss the purification of arbitrary input qubits and arbitrary N qubits. Our scheme only uses linear optical elements and the proposal may be useful in transmission of photons in fibres. This scheme is feasible in the laboratory with the current experimental technology.
We experimentally demonstrate a single-qubit decohering quantum channel using linear optics. We implement the channel, whose special cases include the familiar amplitude-damping channel and the bit-flip channel, using a single, static optical setup. Following a recent theoretical result (Piani et al 2011 Phys. Rev. A 84 032304), we realize the channel in an optimal way, maximizing the probability of success, i.e. the probability for the photonic qubit to remain in its encoding. Using a two-photon entangled resource, we characterize the channel using ancilla-assisted process tomography and find average process fidelities of 0.98 ± 0.01 and 0.976 ± 0.009 for amplitude-damping and the bit-flip case, respectively.
Abstract We report on the first experimental realization of the single qubits purification protocol [J. I. Cirac, A. K. Ekert, and C. Macchiavello, Phys. Rev. Lett. 82, 4344 (1999)] for two copies of a qubit sent through a depolarizing channel. The purification of the polarization‐encoded photonic qubits is achieved with passive linear optical elements. Our experimental results suggest that the present approach may represent a viable alternative to quantum error correction or entanglement distillation.
This thesis deals with the implementation of quantum channels using linear optics. We begin with overviews of some important concepts in both quantum information and quantum optics. First, we discuss the quantum bit and describe the evolution of the states via quantum channels. We then discuss both quantum state and process tomography, methods for how to determine which states and operations we are experimentally implementing in the lab. Second, we discuss topics in quantum optics such the generation of single photons, polarization entanglement, and the construction of an entangling gate. \n \nThe first experiment is the implementation of a quantum damping channel, which intentionally can add a specific type and amount of decohering noise to a photonic qubit. Specifically, we realized a class of quantum channels which contains both the amplitude-damping channel and the bit-flip channel, and did so with a single, static, optical setup. Many quantum channels, and some gates, can only be implemented probabilistically when using linear optics and postselection. Our main result is that the optical setup achieves the optimal success probability for each channel. Using a novel ancilla-assisted tomography, we characterize each case of the channel, and find process fideilities of 0.98pm0.010.98 \\pm 0.010.98pm0.01 for the amplitude-damping channel and 0.976pm0.0090.976 \\pm 0.0090.976pm0.009 for the bit-flip. \n \nThe second experiment is an implementation of a protocol for quantum computing on encrypted data. The protocol provides the means for a client with very limited quantum power to use a server's quantum computer while maintaining privacy over the data. We perform a quantum process tomography for each gate in a universal set, showing that only when the proper decryption key is used on the output states, which is hidden from the server, then the action of the quantum gate is recovered. Otherwise, the gate acts as the completely depolarizing channel.