How weak values emerge in joint measurements on cloned quantum systems

Abstract

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The joint probabilities for non-commuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and post-selection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.

4 pages, major changes to title and introduction, improved explanation of weak measurement statistics

References in corpus (10)

• Direct Measurement of the Quantum Wavefunction
• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• Direct measurement of general quantum states using weak measurement
• Weak values and the Leggett-Garg inequality in solid-state qubits
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• The significance of the imaginary part of the weak value
• Quantum theory of successive projective measurements
• Measuring measurement--disturbance relationships with weak values
• Strange Weak Values

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