Generalization And Application Of Weak Value And Weak Measurement

Quantum measurement theory is one of the axioms of quantum mechanics. Ac-cording to different standards of classification, the quantum measurement could be categorized into orthogonal measurement and non-orthogonal measurement, direct measurement and indirect measurement, or weak measurement and strong measure-ment etc. Therein, the weak measurement, together with its result-weak value, was proposed recently. Weak measurement, based on the indirect measurement the-ory, takes place in the pre-and post-selection context where the measured system and the probe system weakly interact, and thus the outcome of the probe is the weak value. Different from eigenvalues and expectations of observables, weak value could lie far outside the range of eigenvalues, and even be a complex number.Weak measurement and weak value are widely employed in both theoretical and experimental physics, e.g. the application in researches of accurate measurement, detection of quantum state, superluminal phenomena, quantum communication and computation, and two-state vector formalism approach to quantum mechanics etc. The elegant formula of weak value evokes the further research on the’value’in quantum mechanics, and some new conceptions such as modular value, contextual value, and context description of W-operator formalism etc. Weak measurement and weak value are expected to be generalized further more to the cases of nonlocal weak value, symmetric pre-and post-selection of general state, orthogonal pre-and post-selection, and reconstruction of weak value without weak measurement to attain some more general ’value’ etc.In this paper, some efforts to explore the generalization and application of weak measurement and weak value have been made. Regarding weak value, we give the requirements of coupling and reading operators to read out the real and imaginary part of weak value; derive the formula under pre-and post-selection of general state based on the physics nature of weak measurement, point out that there is no possibility for this formula to hold the symmetric pre-and post-selection and apply it in the research ol quantum measurement chain; then discuss the eflect oi operator on the relationship between weak value and some physics quantities. Regarding weak measurement, we make researches on the application of orthogonal pre-and post-selection, which is the limitation of weak measurement and does not produce a weak value. Considering an entangled2×2system of which we choose a subsystem as a probe to witness the weak measurement of an ancilla under orthogonal pre-and post-selection, we derive the quantitive condition to augment the entanglement of the2×2system. This is a generalization of the entangled probe model, which could be used in entanglement concentration.