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Register a new userProtecting an optical qubit against photon loss
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Added by
Wojciech Wasilewski
Publication date
2007
fields
Physics
and research's language is
English
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We consider quantum error-correction codes for multimode bosonic systems, such as optical fields, that are affected by amplitude damping. Such a process is a generalization of an erasure channel. We demonstrate that the most accessible method of transforming optical systems with the help of passive linear networks has limited usefulness in preparing and manipulating such codes. These limitations stem directly from the recoverability condition for one-photon loss. We introduce a three-photon code protecting against the first order of amplitude damping, i.e. a single photon loss, and discuss its preparation using linear optics with single-photon sources and conditional detection. Quantum state and process tomography in the code subspace can be implemented using passive linear optics and photon counting. An experimental proof-of-principle demonstration of elements of the proposed quantum error correction scheme for a one-photon erasure lies well within present technological capabilites.
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Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no universal approach to finding new or optimal codes for a certain task and subject to specific experimental constraints. In particular, once found, a QECC is typically used in very diverse contexts, while its resilience against errors is captured in a single figure of merit, the distance of the code. This does not necessarily give rise to the most efficient protection possible given a certain known error or a particular application for which the code is employed. In this paper, we investigate the loss channel, which plays a key role in quantum communication, and in particular in quantum key distribution over long distances. We develop a numerical set of tools that allows to optimize an encoding specifically for recovering lost particles without the need for backwards communication, where some knowledge about what was lost is available, and demonstrate its capabilities. This allows us to arrive at new codes ideal for the distribution of entangled states in this particular setting, and also to investigate if encoding in qudits or allowing for non-deterministic correction proves advantageous compared to known QECCs. While we here focus on the case of losses, our methodology is applicable whenever the errors in a system can be characterized by a known linear map.
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and in the one-way quantum computer model, the smallest non-trivial quantum codes to tackle this problem. In the experiment, we encode single-qubit input states into highly-entangled multiparticle codewords, and we test their ability to protect encoded quantum information from detected one-qubit loss error. Our results prove the in-principle feasibility of overcoming the qubit loss error by quantum codes.
The problem of combating de-coherence by weak measurements has already been studied for the amplitude damping channel and for specific input states. We generalize this to a large four-parameter family of qubit channels and for the average fidelity over all pure states. As a by-product we classify all the qubit channels which have one invariant pure state and show that the parameter manifold of these channels is isomorphic to $S^2times S^1times S^1$ and contains many interesting subclasses of channels. The figure of merit that we use is the average input-output fidelity which we show can be increased up to $30$ percents in some cases, by tuning of the weak measurement parameter.
Quantum mechanics postulates that measuring the qubits wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate that the qubit collapsed into. We show that this picture breaks down when the qubit is strongly driven during measurement. More specifically, for a fast evolving qubit the measurement returns the time-averaged expectation value of the measurement operator, erasing information about the initial state of the qubit, while completely suppressing the measurement back-action. We call this regime `quantum rifling, as the fast spinning of the Bloch vector protects it from deflection into either of its eigenstates. We study this phenomenon with two superconducting qubits coupled to the same probe field and demonstrate that quantum rifling allows us to measure either one of the qubits on demand while protecting the state of the other from measurement back-action. Our results allow for the implementation of selective read out multiplexing of several qubits, contributing to the efficient scaling up of quantum processors for future quantum technologies.
The exchange interaction between identical qubits in a quantum information processor gives rise to unitary two-qubit errors. It is shown here that decoherence free subspaces (DFSs) for collective decoherence undergo Pauli errors under exchange, which however do not take the decoherence free states outside of the DFS. In order to protect DFSs against these errors it is sufficient to employ a recently proposed concatenated DFS-quantum error correcting code scheme [D.A. Lidar, D. Bacon and K.B. Whaley, Phys. Rev. Lett. {bf 82}, 4556 (1999)].
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