We show that noiseless attenuation combined with noiseless amplification allows multi-partite entangled states to be conditionally transmitted across lossy channels with arbitrarily high fidelity. In special cases (e.g., W states), noiseless amplification alone is sufficient.
Recent work by Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al. [Phys. Rev. Lett. 109, 180503 (2012)] suggests that pairing noiseless amplification with noiseless attenuation can conditionally suppress loss terms in the direct transmission of quantum states. Here we extend this work to entangled states: First, we explore bipartite states, specifically the two-mode squeezed vacuum and NOON states, and, second, we examine M-partite states, concentrating on W and Greenberger-Horne-Zeilinger (GHZ) states. In analogy with the original proposal, our results demonstrate that in each case under consideration, a correct combination of attenuation and amplification techniques before and after transmission through a pure loss channel can restore the initial quantum state. However, we find that for both W and NOON states, the noiseless attenuation is redundant and not required to achieve loss term suppression. This work clarifies the role of noiseless attenuation when paired with noiseless amplification for entanglement distribution and provides an operational example of how GHZ and W state entanglement differs.
Large-scale quantum networking systems will inevitably require methods to overcome photon loss. While the no-cloning theorem forbids perfect and deterministic amplification of unknown quantum states, probabilistic heralded amplification schemes offer a viable path forward. Yet, for over a decade, successful multi-photon state amplification has remained out of reach, despite the fundamental importance of such states in achieving quantum advantage in optical applications. Here, we experimentally demonstrate a high-fidelity and post-selection-free amplifier for multi-photon states. We achieve heralded amplification of states with up to two photons in a single optical mode, with over a hundredfold intensity gain, and verify the coherence-preserving operation of our scheme. Our approach is scalable to higher photon numbers and enables noiseless amplification of complex multi-photon quantum states, with applications in large-scale quantum communication systems, distributed quantum metrology, and information processing.
The losses in a bosonic channel are the primary source of errors in current optic quantum communications. Astonishingly, by combining the noiseless attenuation and noiseless linear amplification, Mi\ifmmode \check{c}\else \v{c}\fi{}uda et al. showed that the unavoidable losses in optic links can be compensated in a nondeterministically but heralded way (M. Micuda, I. Straka, M. Mikova, M. Dusek, N. J. Cerf, J. Fiurasek, and M. Jezek, arXiv:1206.2852). Here we analyze their noiseless loss suppression scheme in a more realistic scenario in which conventional on-off photon detectors as well as the heralded single photon are involved. We use the Wigner function method and investigate the performance of loss suppression in all Fock state space. The noiseless loss suppression for transmitting a weak coherent and single-mode squeezing state are investigated. All these results show that the noiseless attenuation and noiseless linear amplification, if combined, could help to eliminate the channel loss and could be beneficial in future quantum communication.