Information gain versus state disturbance for a single qubit

Abstract

The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state disturbance and the information gain which satisfy certain invariance conditions. This class includes in particular the Shannon entropy versus the operation fidelity. The central role in the derivation is played by efficient quantum operations, which leave the system in a pure output state for any measurement outcome. It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.

17 pages, LaTeX, osid.sty. Substantially expanded and generalized

References in corpus (8)

• Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Fidelity balance in quantum operations
• Information Tradeoff Relations for Finite-Strength Quantum Measurements
• Reversible quantum operations and their application to teleportation
• Optimal quantum teleportation with an arbitrary pure state
• Optimal minimal measurements of mixed states
• Fidelity trade-off for finite ensembles of identically prepared qubits

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• Information, fidelity, and reversibility in general quantum measurements
• The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
• Measurement uncertainty from no-signaling and non-locality
• An effective iterative method to build the Naimark extension of rank-n POVMs
• Transferring elements of a density matrix
• On the properties of information gathering in quantum and classical measurements
• Allowed region and optimal measurement for information versus disturbance in quantum measurements
• Derivative of the disturbance with respect to information from quantum measurements
• Complementary Relationships between Entanglement and Measurement
• Local trade-off between information and disturbance in quantum measurements
• Recycling of quantum information: Multiple observations of quantum systems