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In a classical world, simultaneous measurements of complementary properties (e.g. position and momentum) give a systems state. In quantum mechanics, measurement-induced disturbance is largest for complementary properties and, hence, limits the precision with which such properties can be determined simultaneously. It is tempting to try to sidestep this disturbance by copying the system and measuring each complementary property on a separate copy. However, perfect copying is physically impossible in quantum mechanics. Here, we investigate using the closest quantum analog to this copying strategy, optimal cloning. The coherent portion of the generated clones state corresponds to twins of the input system. Like perfect copies, both twins faithfully reproduce the properties of the input system. Unlike perfect copies, the twins are entangled. As such, a measurement on both twins is equivalent to a simultaneous measurement on the input system. For complementary observables, this joint measurement gives the systems state, just as in the classical case. We demonstrate this experimentally using polarized single photons.
It is often said that measuring a systems position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a weak-measurement, this disturbance can be reduced. One might expect this
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapun
We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and prese
we envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch exist in a superposition of com
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in quantum technolo