Convex approximations of quantum channels

Abstract

We address the problem of optimally approximating the action of a desired and unavailable quantum channel $\Phi$ having at our disposal a single use of a given set of other channels $\{{\Psi }_i\}$. The problem is recast to look for the least distinguishable channel from $\Phi$ among the convex set ${\sum }_i{p}_i{\Psi }_i$, and the corresponding optimal weights $\{p_i\}$ provide the optimal convex mixing of the available channels $\{{\Psi }_i\}$. For single-qubit channels we study specifically the cases where the available convex set corresponds to covariant channels or to Pauli channels, and the desired target map is an arbitrary unitary transformation or a generalized damping channel.

arXiv comment6 pages, 5 figures

References in corpus (18)

• Distance measures to compare real and ideal quantum processes
• Quantum cloning
• The Quantum Chernoff Bound
• Programmable quantum gate arrays
• Statistical distinguishability between unitary operations
• Using entanglement improves precision of quantum measurements
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Optimal discrimination of quantum operations
• Factorization and dilation problems for completely positive maps on von Neumann algebras
• Experimental observation of weak non-Markovianity
• Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations
• Universal measurement apparatus controlled by quantum software
• Operational distance and fidelity for quantum channels
• Efficient universal programmable quantum measurements
• Experimental detection of quantum channel capacities
• Approximate programmable quantum processors
• Physical realizations of quantum operations
• Purification of noisy quantum measurements

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• The optimal approximation of qubit states with limited quantum states
• Probabilistic unitary synthesis with optimal accuracy
• The best approximation of an objective state with a given set of quantum states
• The best approximation of a given qubit state with the limited pure-state set
• Zero-Noise Extrapolation via Cyclic Permutations of Quantum Circuit Layouts