Simple approach to approximate quantum error correction based on the transpose channel
نویسندگان
چکیده
We demonstrate that there exists a universal, near-optimal recovery map—the transpose channel—for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.
منابع مشابه
Entanglement and Approximate Quantum Error Correction
The possibility of performing quantum error correction obviously lies behind and justifies the vast efforts made up to now in order to develop quantum computation techniques, since it allows fault-tolerant computationeven when quantum systems—in fact extremely sensitive to noise—are considered as the basic carriers of information. Besides well-known algebraic conditions for exact quantum error ...
متن کاملGENERALIZED JOINT HIGHER-RANK NUMERICAL RANGE
The rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. In this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, Generaliz...
متن کاملApproximate quantum error correction, random codes, and quantum channel capacity
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This result is then used to analyze the average error correcting performance of codes that are randomly drawn from unitarily invariant code ensembles. Our results co...
متن کاملApproximate Quantum Error Correction
X iv :q ua nt -p h/ 01 12 10 6v 1 1 8 D ec 2 00 1 Approximate quantum error correction Benjamin Schumacher and Michael D. Westmoreland February 1, 2008 Department of Physics, Kenyon College, Gambier, OH 43022 USA Department of Mathematical Sciences, Denison University, Granville, OH 43023 USA Abstract The errors that arise in a quantum channel can be corrected perfectly if and only if the chann...
متن کاملApproximate Quantum Error Correction Revisited: Introducing the Alphabit
We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap bet...
متن کامل