Foundations and Applications of Finite Strength Quantum Measurement and Weak Value

Abstract

Quantum measurement is analyzed from a conceptual point of view by comparing weak and strong interaction regimes using von-Neumann’s measurement model and explicit conditions for weakness have been derived for both weak value and expectation value. The effect of a weak interaction up to strength of orders 1 and 2 without post-selection on the system and pointer states is studied. This engenders a simple interpretation of the imaginary part of the weak value. A general mathematical formalism of weak measurement within which previous results fit is derived. Effect of multiple degrees of freedom and correlations among these within the pointer states in the context of weak measurement is reviewed. Weak measurement is studied as a tool to create entanglement between previously uncorrelated quantum states. A mathematical formalism irrespective of the pointer state used is derived under which one can obtain the joint weak value of incompatible observables as well as second order of the weak values. Using a bipartite correlated resource state, a protocol for determination of weak value corresponding to a weak interaction done by one party by another spatially separated party is conceptualized and mathematically demonstrated.