Alladi Ramakrishnan Hall

Pre-synopsis talk

Sahil

IMSc

In this talk, I will present applications of pre- and post-selected (PPS) systems and show existence of uncertainty relations for incompatible observables. I will provide several methods to extract product and higher moment weak values in PPS systems. I will use product and higher moment weak values to reconstruct quantum states of single and bipartite systems. Further, a necessary separability criteria to detect entanglement using product weak values will also be derived. Because of the growing applications of PPS systems, it is important to characterize the behaviour of incompatible observables in the form of uncertainty relations, which I will derive by defining a standard deviation of an observable in a PPS system. I will show that the PPS system can exhibit more bizarre behaviours than the usual ones. For example, two compatible observables can disturb each other’s measurement results in a PPS system. It is also possible that a quantum state can be prepared in a PPS system for which both of the standard deviations of incompatible observables are zero although this is not possible in the standard quantum system. I will provide physically relevant applications of our uncertainty relations. In a PPS system, I will show that skew information of an observable can be measured using the notion of weak values. Because skew information is observable dependent, I will derive state-dependent (with explicit form of the commutator of incompatible observables) and state-independent uncertainty relations. I will derive uncertainty equality based on standard deviation for incompatible operators with mixed states, a generalization of previous works in which only pure states were considered.