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Optimal recovery quantum error correction
Optimal recovery quantum error correction













optimal recovery quantum error correction

Retzker, Increasing sensing resolution with error correction, Phys. Ozeri, Heisenberg limited metrology using quantum error-correction codes. Kraus, Improved quantum metrology using quantum error correction, Phys. Lukin, Quantum error correction for metrology, Phys. Maccone, Using entanglement against noise in quantum metrology, Phys. Durkin, True limits to precision via unique quantum probe, arXiv:1402.0495 (2014). Demkowicz-Dobrzański, Efficient tools for quantum metrology with uncorrelated noise, New J. Guţă, The elusive heisenberg limit in quantum-enhanced metrology, Nat. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nat. Walmsley, Quantum phase estimation with lossy interferometers, Phys. Imai, A fibre bundle over manifolds of quantum channels and its application to quantum statistics, J. Bartlett, Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement, Phys. Wiseman, Optimal states and almost optimal adaptive measurements for quantum interferometry, Phys. Cirac, Improvement of frequency standards with quantum entanglement, Phys. Maccone, Quantum-enhanced measurements: beating the standard quantum limit, Science 306, 1330 (2004). Wineland, Toward heisenberg-limited spectroscopy with multiparticle entangled states, Science 304, 1476 (2004). Heinzen, Optimal frequency measurements with maximally correlated states, Phys. Lam, Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection, Phys. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Dowling, A quantum rosetta stone for interferometry, J. Burnett, Interferometric detection of optical phase shifts at the heisenberg limit, Phys. Caves, Quantum-mechanical noise in an interferometer, Phys. Lloyd, Advances in photonic quantum sensing, Nat. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Schnabel, Squeezed states of light and their applications in laser interferometers, Phys. Apellaniz, Quantum metrology from a quantum information science perspective, J. Maccone, Advances in quantum metrology, Nat. Paris, Quantum estimation for quantum technologies, Int. In the context of this question, in the non autonomous scenario, if ancillae are found in $|00\rangle$, the density matrix of data qubits will become $P_0 \rho P_0/Tr(\rho P_0)$, if the ancillae are found in $|01\rangle$, the density matrix of data qubits will becomes $P_3 \rho P_3/Tr(\rho P_3)$ and so on.V. Thus such projection has a probability $0$ to occur. In your example, in your comment you would find $Tr(\rho P_2)=0$ for $\rho=|\psi_e \rangle \langle \psi_e |$ that you defined. Indeed, as you see, you must compute a probability of outcome for each of the projector. In practice all the projectors play a role in the measurement. $$ \rho \to P_k \rho P_k/ Tr(\rho P_k)$$ with probability $p_k = Tr(\rho P_k)$ If you measure (and read the outcome), the density matrix will be transformed as: In the case of the simple three-qubit repetition code, the encoding consists of the mappings $|0\rangle \rightarrow\left|0_$ verifying $\sum_k P_k = I$.















Optimal recovery quantum error correction