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We introduce the idea that the knowable quantum reality depends not only onthe state but also on measurements. Mathematically, we map the states from theordinary Hilbert space into new states in what we call the measurement space.The state vectors in the measurement space contain only the informationaccessible with a particular set of measurements. The space can be used to findthe operational equivalent of any information theoretic quantity. We use theformalism to define the operationally meaningful entanglement, explore itsproperties and apply it to mode entanglement. There we find that amode-entangled state of a single particle has no operationally usefulentanglement unless additional degrees of freedom are introduced to the system.

Introduction to Measurement Space and Application to Operationally Useful Entanglement and Mode Entanglement