Determining complementary properties with quantum clones

Abstract

In a classical world, simultaneous measurements of complementary properties (e.g. position and momentum) give a system's 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 system's state, just as in the classical case. We demonstrate this experimentally using polarized single photons.

5+4 pages, 3+5 figures (includes SM)

References in corpus (7)

• Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence
• A quantum Fredkin gate
• Dynamics of simultaneously measured non-commuting observables
• Direct measurement of the density matrix of a quantum system
• Simultaneous tracking of spin angle and amplitude beyond classical limits
• Quantum-coherent mixtures of causal relations
• Experimental realization of linear-optical partial SWAP gates

Cited by in corpus (13)

• Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
• Properties and Applications of the Kirkwood-Dirac Distribution
• Quantum process tomography of a high-dimensional quantum communication channel
• Cloning of Quantum Entanglement
• Local measurement uncertainties impose a limit on non-local quantum correlations
• Determining complementary properties using weak-measurement: uncertainty, predictability, and disturbance
• Statistical signatures of quantum contextuality
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Quantum coherence and negative quasi probabilities in a contextual three-path interferometer
• Optimal simultaneous measurements of incompatible observables of a single photon
• Virtual Cloning of Quantum States
• An exploration of the limits of control using quantum superpositions