Device-independent certification of the teleportation of a qubit

Abstract

We want to certify in a black box scenario that two parties simulating the teleportation of a qubit are really using quantum resources. If active compensation is part of the simulation, perfect teleportation can be faked with purely classical means. If active compensation is not implemented, a classical simulation is necessarily imperfect: in this case, we provide bounds for certification of quantumness using only the observed statistics. The usual figure of merit, namely the average fidelity of teleportation, turns out to be too much of a coarse-graining of the available statistical information in the case of a black-box assessment.Introduction.-Shortly after the milestone paper that introduced quantum teleportation [1], the question was asked of which deviation from the ideal case one can tolerate while still claiming that proper quantum effects are being observed. Popescu proved that, if Alice and Bob share no entanglement, the average fidelity for the teleportation of unknown qubit states is bounded byF = 2

Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states

“…(14), into M copies of the output GPCS |ψ * g . For the complex conjugation of GPCSs, the optimal quantum fidelity can be obtained from Eq.…”

“…Other studies focused on numerical methods (e.g., based on semidefinite programming) to derive teleportation benchmarks for more realistic sets of possibly mixed input states [13]. Very recently, device-independent benchmarks for teleportation of qubit states were investigated [14]. Benchmarks applicable to other protocols have been developed as well.…”

Continuous-variable versus hybrid schemes for quantum teleportation of Gaussian states

“…One product of the focus on quantum teleportation has been the development of teleportation benchmarks [26][27][28][29][30][31][32][33][34][35][36]. Put crudely, these benchmarks determine how good a teleportation-like procedure must be such that it could have been performed only with a shared entangled resource.…”

Self-testing mutually unbiased bases in higher dimensions with space-division multiplexing optical fiber technology

“…( 8) and measure it in the basis defined by the orthorgonal states of Eq. (10). Fiber-based polarization controllers (not shown for the sake of simplicity) are used in each path to guarantee the indistinguishability of the core modes, such that there is no path-information available to compromise the visibility of the interferometer [62,63].…”

“…Furthermore, these verification methods should be possible to perform efficiently, and using only classical resources. Consequently, they are currently the subject of intensive study in the quantum information community [5][6][7][8][9][10][11][12], where they are commonly referred to as self-testing protocols. The strongest method is known as the "deviceindependent approach", which involves two parties sharing an entangled quantum state, and the only considered assumption for self-testing the proper implementation of a given task is that these parties are space-like separated.…”