Teleportation fidelity as a probe of sub-Planck phase-space structure

Abstract

We investigate the connection between sub-Planck structure in the Wigner function and the output fidelity of continuous-variable teleportation protocols. When the teleporting parties share a two-mode squeezed state as an entangled resource, high fidelity in the output state requires a squeezing large enough that the smallest sub-Planck structures in an input pure state are teleported faithfully. We formulate this relationship, which leads to an explicit relation between the fine-scale structure in the Wigner function and large-scale extent of the Wigner function, and we treat specific examples, including coherent, number, and random states and states produced by chaotic dynamics. We generalize the pure-state results to teleportation of mixed states.

19 pages, 5 figures

References in corpus (3)

• Experimental demonstration of quantum teleportation of broadband squeezing
• Quantum metrology at the Heisenberg limit with ion traps
• Time-frequency Domain Analogues of Phase Space Sub-Planck Structures

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• Superposing compass states for asymptotic isotropic sub-Planck phase-space sensitivity
• Enhanced Quantum Sensitivity in a Vibrating Diatomic Molecule due to Rotational Amendment
• Sub-shot-noise sensitivity via superpositions of two deformed kitten states
• Nonclassicality and sub-Planck structures of photon subtracted compass states