Peer review of: Orbital angular momentum multiplexed deterministic all-optical quantum teleportation (2020)

Reviewers' Comments: 
 
Reviewer #1: 
Remarks to the Author: 

The authors set out to demonstrate teleportation of states within a 9 dimensional subset of orbital 
angular momentum modes, following from their recent work on entanglement via FWM in an 
atomic vapour. This is a timely and technologically exciting idea, expanding on the first 
demonstration of 3D teleportation (realised as path encoding) which was published only last year 
by Yi-Han Luo et al. (Quantum Teleportation in High Dimensions, DOI: 
10.1103/PhysRevLett.123.070505) - a paper that the authors curiously do not cite. 
The "all-optical teleportation" scheme used in this manuscript is based on a theoretical proposal 
from 1999 which was until now not known to me. It is notably different from conventional 
teleportation. Rather than sending information on the measurement outcome on Alice's state 
together with one of the EPR twin photons, here the amplified state itself is sent via a classical 
channel, seeming closer to "portation" rather than "teleportation". The fidelity that can be reached 
in this scheme is inherently limited by vacuum noise in addition to detector noise. 
While I find the experiment presented in the manuscript appealing, and potentially suitable for 
publication in Nature Communications, the manuscript is missing 
- a clear description of the teleportation scheme, 
- details on the atomic processes for the EPR pair generation and in particular the operation of the 
parametric amplifier, 
- a more thorough theoretical analysis, 
- an explanation why a continuous variable scheme is required for states described in a subset of a 
discrete Hilbert space, 
- experimental details on the generation of the state to be teleported. 
 
 
 
Reviewer #2: 
Remarks to the Author: 
The manuscript by S. Liu reports the experimental demonstration of the continuous variable 
teleportation protocol realised using entangled orbital angular momentum (OAM) modes of light 
beams. The teleportation scheme implemented is the all-optical quantum teleportation proposed 
by T. Ralph in 1999. Instead of Bell state measurements and feed-forward, all-optical quantum 
teleportation requires linear amplification of the input state. In the present experiment, the linear 
amplifier is replaced by an OAM mode-matched parametric amplifier. The paper shows that 
teleportation can be established using OAM modes up to the topological charge of 4, beating the 
classical fidelity limit. The teleportation of OAM mode superpositions has also been demonstrated, 
showing the possibility to achieve simultaneous teleportation of OAM modes. 
 
The paper is very interesting and I support its publication in Nature Communications; however, I 
have some comments and questions that should be addressed before final acceptance. 
 
1) In the description of the experiment (Results section), the EPR source should be pumped with a 
Gaussian beam but is not specified. About this I have a curiosity that could be interesting for 
clarifying the generation mechanism. Which is the limiting factor in using a smaller waist? Is it 
useful to improve the parametric gain and the squeezing? 
 
2) Somehow related to the question above, the EPR source seems to be the main limitation in the 
maximum topological charge that can be reached for quantum teleportation as shown in Fig 3. The 
author should explain how the pump beam can influence the EPR correlations between OAM 
modes. 
 
3) The local oscillator beam is not described in Fig. 1, some descriptions should also be given along 
with the text. How it is obtained? How much is the local oscillator power? In which way the its 
phase is locked? 
 
4) The quantum efficiency of the homodyne detector is not reported. 
 
5) The implementation of all-optical quantum teleportation requires a linear amplifier. Instead, 
here a seeded noncollinear parametric amplifier based on FWM is used. Some clarification should 
be given along the main text. It would be useful to insert a comment on the equivalence of both 
approaches. In which way the fidelity is influenced by the noise added during the amplification 
process? Is the amplifier pump noise also a limiting factor? 
 
6) The caption of Fig. 1: the notation $|\alpha_in> (\hat a_in)$ is not clear, it should be replaced 
by mode $\hat a_in$ populated by a coherent state $|\alpha_in>$. Fig. 1 should be changed 
accordingly. There is a double Rb in the caption. 
 
7) It is not clear how the inseparability is calculated. Some clarifications should be given together 
with references. 
 
8) In Fig.2 the insets of Fig.2c and Fig.2d are not clearly described. The meaning of left, center, 
and right beams should be explained. 
 
 
 
Reviewer #3: 
Remarks to the Author: 
The paper presents the experimental results of an all-optical (OA) teleportation protocol, where a 
coherent state encoded on an orbital angular momentum (OAM) mode of light (\ell=1) is 
teleported with Fidelity~0.61 (beating the classical limit, i.e., F=0.5). Even though the achieved 
Fidelity is less than the corresponding one achieved through the (conventional) Braunstein-Kimble 
(BK) protocol, i.e, F~0.83 [M. Yukawa et al., Phys. Rev. A 77, 022314 (2008)], this is an 
important result, since (to my knowledge) that's the first time that the OA teleportation protocol 
has been experimentally demonstrated, so further progress and higher Fidelities should be 
expected in the future. The results of this work can potentially make this alternative way to 
perform teleportation widely known to the community, and other research groups might follow up 
in the future in order to achieve even higher values of fidelity. Another important result of this 
work is the experimental demonstration of parallel AO teleportation of two coherent modes 
(corresponding to different topological charges of OAM), which can be used to to increase the 
quantum capacity of quantum channels. 
 
The manuscript is well-written and it is worth to be published in Nature Communications for the 
reasons mentioned before, however, there is a specific claim in the paper regarding the security of 
the teleportation that I would strongly advise to be removed. 
 
In particular, the authors argue that if we block the arm of the entangled state that goes to Bob, 
then Bob acts as an eavesdropper (Eve), and under this modification, the new measured 
Fidelity~0.37 lies below the classical limit (F=0.5), and thus they show security against 
eavesdropping. However, that's not the right way of assessing security in a teleportation protocol. 
Following the discussion of Ref.[F. Grosshans and P. Grangier, Phys. Rev. A 64, 010301(R) (2001)] 
(or the more recent analysis that connects the security of the teleportation with the 
entanglement/steering shared between Alice and Bob in Ref.[Q. He et al., Phys. Rev. Lett. 115, 
180502 (2015)]), the security of the teleported state is related to Alice's ability to cheat by cloning 
the initial state. In particular, let us assume that Alice can perfectly perform a quantum cloning 
protocol, and thus achieve two clones of the initial state with Fidelities of 2/3 each. Then in 
principle she can perfectly teleport one of her clones to Bob. However, since Bob doesn't know that 
Alice cheated, he measures F=2/3. Thus, in order Bob to be sure that his state is better than any 
other potential clones he needs to achieve a fidelity higher than 2/3 (also known as the no-cloning 
limit). Another way of looking at the same problem is by assuming that Eve has full access to the 
losses along at least one arm of the entangled state (along with her access to the classical channel 
between Alice and Bob). Then Eve's best strategy is to build her own version of the teleported 
state. If the transmissivity of the channel is below 1/2 then Eve can create a better copy than Bob, 
which again means that F>2/3 is required for a secure teleportation. 
 
I also have a question regarding the results of the parallel OA teleportation. More specifically, in 
Fig.4(a) a Fidelity~0.63 is reported for the superposition of modes \ell=-1 and \ell=1. I find it 
really weird that this fidelity is higher than the fidelity reported for the single teleported mode 
\ell=1, i.e., F~0.61. I would assume that teleporting a superposition of modes is a harder task (as 
it is actually shown later in Fig.(b)-(d) with Fidelities ranging from ~0.54 to ~0.6). It would be 
nice if the authors could provide an explanation for this counter-intuitive result. 
 
Below, I also have a list of further (minor) suggestions: 
 
1. The first sentence in the abstract "Quantum teleportation is the most essential and fascinating 
protocol in quantum information." should be toned down a bit, and rewritten as "one of the most 
essential..." 
 
2. Right after Eq.(2) the authors should clearly state that the two last terms in Eq.(2) vanish in the 
limit of an EPR entangled state and very high parametric gain, leaving as an output state only the 
first term, which is equal to the input state, thus we achieve teleportation. 
 
3. In Fig.3 a comparison between the established entanglement and the achieved fidelity for the 
differen OAM modes is presented. It is true that in the literature the separability criterion (or the 
logarithmic negativity, which is a monotonic function of the maximum possible violation of the 
separability criterion) has been extensively used to "measure" entanglement, but there are more 
rigorous ways to quantify entanglement, such as: (i) entanglement of formation, (ii) relative 
entropy of entanglement, and (iii) squashed entanglement. 
 
4. I think that the authors should explain the reasoning behind picking a half wave plate to 
represent the all-optical channel between Alice and Bob. 
 
5. The papers [M. Yukawa et al., Phys. Rev. A 77, 022314 (2008)] and [N. Lee et al., Science 332, 
330 (2011)] should be cited in the introduction regarding previous works on experimental 
teleportation results, since they present the current state of the art on BK teleportation 
experiments.