Distilling Gaussian states with Gaussian operations is impossible.

By Jens Eisert, S. Scheel, Martin Bodo Plenio. Physical Review Letters, 2002

471 citations recorded by the source corpus.

We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/322ad87cc6b02f926701a978802a6e5fad28baa3

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Citations in the corpus

Gaussian quantum information (2011, methodology): “However, the distillation of mixed Gaussian states into pure Gaussian states is not possible using only Gaussian LOCC operations (Eisert, Scheel, and Plenio, 2002; Fiuràšek, 2002a;Giedke andCirac, 2002), but canbe achieved using nonGaussian operations that map Gaussian states into Gaussian states…”
Entanglement distillation from Gaussian input states (2010, background): “This is due to the difficulties imposed by the no-go theorem, which states that Gaussian operations alone can never distill entanglement from Gaussian state”
Tomography of quantum detectors (2009, background): “Now that it is well characterized, the photon counter also provides a unique tool for carrying out non-Gaussian operations, which are critical for quantum information processing using the electromagnetic field as the information carrie”
Advances in quantum cryptography (2019, unknown): “One approach has been based on the used of non-Gaussian operations, like noiseless linear amplifiers (NLA) and photon subtraction/addition (whose importance is well-known in entanglement distillation [439]).”
Photon temporal modes: a complete framework for quantum information science (2015, background): “[52] J Eisert, S Scheel, and M B Plenio, “Distilling Gaussian states with Gaussian operations is impossible,” Phys.”
Quantum interface between light and atomic ensembles (2008, background): “In particular it is known that Gaussian operations alone do not allow for distillation of entanglement from Gaussian states (Eisert et al., 2002; Fiurasek, 2002; Giedke and Cirac, 2002) and that algorithms for efficient classical simulation of any evolution involving only Gaussian operation and…”