Steganographic Entanglement Sharing

Bruno Avritzer; Todd A. Brun

arxiv: 2409.09335 · v1 · pith:JQ6BRK62new · submitted 2024-09-14 · 🪐 quant-ph

Steganographic Entanglement Sharing

Bruno Avritzer , Todd A. Brun This is my paper

Pith reviewed 2026-05-23 20:59 UTC · model grok-4.3

classification 🪐 quant-ph

keywords steganographyentanglementquantum teleportationthermal stateseavesdropperoptical channelFock statescoherent states

0 comments

The pith

Steganographic entanglement sharing enables nonclassical state teleportation even with an active eavesdropper present.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper extends prior protocols for disguising classical communications as thermal states of a harmonic oscillator to the case of quantum entanglement. States are prepared and sent in an optical channel so that they remain indistinguishable from ordinary thermal noise, allowing entangled resources to be shared covertly. The central demonstration shows that such hidden entanglement supports teleportation of nonclassical states despite an eavesdropper who may know the protocol or possess additional measurement tools. A reader would care because the approach supplies a concrete method for performing quantum information tasks in monitored channels without revealing the quantum character of the transmission. The work therefore bridges classical steganography techniques with quantum information processing.

Core claim

The paper claims that steganographic entanglement sharing, achieved by disguising entangled Fock and coherent states to mimic thermal states, permits the teleportation of nonclassical states through an optical channel even when an active eavesdropper is present and may hold knowledge of the protocol or extra resources.

What carries the argument

The steganographic protocol that prepares and transmits states indistinguishable from thermal noise while carrying quantum entanglement.

If this is right

Nonclassical states can be teleported without the eavesdropper detecting the presence of quantum correlations.
The optical channel appears purely thermal to the adversary throughout the transmission.
Quantum information tasks become feasible in environments where an active monitor may intercept or measure the channel.
The same disguise technique used for classical messages extends directly to entangled resources.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar disguises could be tested for other quantum communication primitives such as quantum key distribution.
Optical-table experiments with controlled thermal backgrounds would provide a direct check on the indistinguishability assumption.
The protocol might combine with existing error-correction methods to improve robustness against both noise and detection.

Load-bearing premise

The quantum states can be prepared and transmitted such that they remain indistinguishable from thermal states to an active eavesdropper who may possess knowledge of the protocol or additional measurement resources.

What would settle it

A laboratory measurement in which an eavesdropper equipped with the stated resources distinguishes the transmitted states from true thermal states at a rate exceeding the expected thermal fluctuations would falsify the claim.

Figures

Figures reproduced from arXiv: 2409.09335 by Bruno Avritzer, Todd A. Brun.

**Figure 2.** Figure 2: FIG. 2: (a) the Wigner function of the odd cat state with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: (a) the fidelities of GKP state teleportation and (b) Wigner function for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Average result of teleportation of the odd [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: Using the StrawberryFields package, we were able to simulate the results of two-qubit quantum state [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: The maximum measurement probability ( [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: The circuits for continuous variable [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original abstract

In a previous work we have discussed a theoretical grounding for classical steganography using quantum Fock and coherent states in an optical channel, building on previous work by Wu et al. In that work, we discussed protocols which disguise communications to mimic the thermal state of a harmonic oscillator. In this work we will extend this to transmission of quantum information, and demonstrate the utility of steganographic entanglement sharing in practical contexts like nonclassical state teleportation, even with the presence of an active eavesdropper.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper extends the authors' prior classical steganography to quantum entanglement sharing for teleportation but treats indistinguishability from thermal states as given rather than proving it against an active, protocol-aware eavesdropper.

read the letter

The main takeaway is that this work lifts the authors' earlier classical steganography protocol—disguising signals as thermal states using Fock and coherent states—to the quantum case, with the stated goal of enabling entanglement sharing and nonclassical teleportation without detection. The abstract positions the contribution as a direct extension rather than a new foundational technique. What the paper does is identify a potential use case in optical quantum channels where hiding the quantum resource itself could matter for network security. It connects the disguise method to teleportation utility and notes the presence of an active eavesdropper as a motivating scenario. That framing is straightforward and stays within the scope of their previous line of work. The central soft spot is the security claim. The abstract asserts that the transmitted states remain indistinguishable from thermal states even to an active eavesdropper, yet it supplies no trace-distance bound, diamond-norm analysis, or argument that the effective channel to Eve matches the thermal channel under adaptive or collective measurements. If the eavesdropper knows the encoding map, the indistinguishability does not automatically carry over from the classical setting, and nothing in the provided text derives it. There are also no protocol details, error rates, or explicit construction for how the entanglement is prepared, transmitted, and used for teleportation. The paper is therefore mostly conceptual and rests on the prior classical result for its technical grounding. This is for researchers already following the authors' steganography thread who want to see the quantum extension sketched. A reader seeking a worked protocol or security reduction would come away empty. I would not send it to peer review in this form; the security guarantee needs to be turned into an actual derivation before referee time is warranted.

Referee Report

1 major / 0 minor

Summary. The manuscript extends the authors' prior work on classical steganography with quantum Fock and coherent states (which mimic thermal states of a harmonic oscillator) to the transmission of quantum information. It proposes steganographic entanglement sharing as a method to enable nonclassical state teleportation in the presence of an active eavesdropper by ensuring the transmitted states remain indistinguishable from thermal noise.

Significance. If a rigorous security reduction establishing indistinguishability against protocol-aware eavesdroppers can be supplied, the approach would provide a concrete mechanism for covert quantum communication channels that leverage existing thermal noise backgrounds. The work builds directly on the authors' earlier classical-steganography results and the cited Wu et al. framework, but its impact is currently limited by the absence of explicit bounds or protocol details.

major comments (1)

[Abstract] Abstract: the central claim that steganographic entanglement sharing enables nonclassical state teleportation 'even with the presence of an active eavesdropper' is not supported by any security reduction. No trace-distance, diamond-norm, or equivalent bound is given showing that the effective channel to an eavesdropper (who may know the encoding map and perform adaptive or collective measurements) is identical to the thermal channel.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need for a more explicit security analysis. We address the single major comment below.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that steganographic entanglement sharing enables nonclassical state teleportation 'even with the presence of an active eavesdropper' is not supported by any security reduction. No trace-distance, diamond-norm, or equivalent bound is given showing that the effective channel to an eavesdropper (who may know the encoding map and perform adaptive or collective measurements) is identical to the thermal channel.

Authors: We agree that the manuscript does not supply an explicit security reduction (trace distance, diamond norm, or otherwise) establishing that the eavesdropper's effective channel is identical to the thermal channel when the eavesdropper knows the encoding and may employ adaptive or collective measurements. The abstract claim rests on the indistinguishability established for the same state preparation in our prior classical-steganography work, but this is not re-derived or bounded for the entanglement-sharing protocol here. We will revise the abstract to qualify the claim (removing the unqualified reference to an 'active eavesdropper') and add a short discussion section that explicitly references the prior bounds while noting the absence of a new reduction for the quantum-information case. This constitutes a partial revision; a full diamond-norm proof against protocol-aware adaptive adversaries would require additional analysis that we do not claim to provide in the current manuscript. revision: partial

standing simulated objections not resolved

A complete, self-contained security reduction (e.g., diamond-norm bound) against an active, protocol-aware eavesdropper who knows the encoding map is not present in the manuscript and would require substantial new theoretical work beyond the scope of the present extension of the classical results.

Circularity Check

1 steps flagged

Indistinguishability to active eavesdropper reduces to self-cited prior protocol

specific steps

self citation load bearing [Abstract]
"In a previous work we have discussed a theoretical grounding for classical steganography using quantum Fock and coherent states in an optical channel, building on previous work by Wu et al. In that work, we discussed protocols which disguise communications to mimic the thermal state of a harmonic oscillator. In this work we will extend this to transmission of quantum information, and demonstrate the utility of steganographic entanglement sharing in practical contexts like nonclassical state teleportation, even with the presence of an active eavesdropper."

The claim that entanglement sharing works against an active eavesdropper presupposes that the transmitted states produce identical statistics to a thermal state for any measurement (including adaptive/collective ones) even when the eavesdropper knows the encoding. This indistinguishability is imported wholesale from the authors' prior paper rather than re-proven or bounded in the present manuscript.

full rationale

The paper's core security claim (states remain indistinguishable from thermal states to a protocol-aware eavesdropper) is carried entirely by the authors' own prior work on classical steganography. The abstract explicitly states the extension relies on that prior construction without supplying a new trace-distance or diamond-norm bound. This matches self-citation load-bearing: the load-bearing premise is justified only by overlapping-author citation whose content is not re-derived or externally verified here.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no equations, parameters, or assumptions are detailed enough to populate free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5594 in / 941 out tokens · 21689 ms · 2026-05-23T20:59:51.782722+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages · 2 internal anchors

[1]

Inthatwork, itwasdemonstratedthatcoherentstate teleportation could be performed with an asymptotic (in r) average fidelity of1 − p, which for p <

State Teleportation In the case of TMSV state transmission, the channel above is explicitly given by ξp(ρTMSV) = pρth ⊗ ρth + (1 − p)ρTMSV, (11) which is a sort of continuous variable analog of the Werner channel [8], and has been studied previously in [9]. Inthatwork, itwasdemonstratedthatcoherentstate teleportation could be performed with an asymptotic ...

work page
[2]

Superdense Coding There are some other common tasks which make use of entanglement for purposes of communication, such as superdense coding. It should be noted that continu- ous variable superdense coding via sending TMSV states through the monitored channel is not a task which can be performed steganographically, even in principle (at least with a perfec...

work page
[3]

D(x p 2) |0Evei | Evei Alice Bob Eve T=.1 Expectations of Paulis Pauli Noiseless Rotated W+R (.1) W+R (.01) XX 0.9928 0.6320 0.3238 0.6189 XZ 0.0239 0.6624 0.3396 0.6692 ZX -0.0147 -0.6002 -0.3100 -0.5744 ZZ 0.9893 0.6570 0.3458 0.6557 S 1.991 2.551 1.319 2.518 FIG. 5: Using the StrawberryFields package, we were able to simulate the results of two-qubit q...

work page
[4]

This is intuitive: you can imagine that Bob no longer has a communication advantage against Eve, and therefore there cannot be a quantum advantage either

State Teleportation Ifwereexaminethecatstateteleportationprotocol, we see in Figure 4 that atη = .5 there is no longer negativity to be observed. This is intuitive: you can imagine that Bob no longer has a communication advantage against Eve, and therefore there cannot be a quantum advantage either. To formalize this argument, we can examine the notion of...

work page
[5]

Superdense Coding Figure 7 shows that steganographic superdense cod- ing is impossible under this eavesdropper model, since you must always send correlated information through the channel which Eve can store and detect using a joint measurement. This is in contrast to the Werner channel; while in theory Eve could hold a state in that channel as well, Alic...

work page
[6]

Avritzer and T

B. Avritzer and T. A. Brun, Quantum steganography via coherent- and fock-state encoding in an optical medium, Phys. Rev. A109, 032401 (2024)

work page 2024
[7]

B. B. Wu and E. E. Narimanov, A method for secure communications over a public fiber-optical network, Opt. Express 14, 3738 (2006)

work page 2006
[8]

B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, Optical steganography based on amplified spontaneous emission noise, Opt. Express 21, 2065 (2013)

work page 2065
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A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, On-chip optical squeez- ing, Phys. Rev. Applied3, 044005 (2015)

work page 2015
[10]

C. A. Fuchs and J. van de Graaf, Cryptographic distin- guishability measures for quantum mechanical states, "" (1997), arXiv:quant-ph/9712042

work page internal anchor Pith review Pith/arXiv arXiv 1997
[11]

Killoran, J

N. Killoran, J. Izaac, N. Quesada, V. Bergholm, M. Amy, and C. Weedbrook, Strawberry Fields: A Software Plat- form for Photonic Quantum Computing, Quantum3, 129 (2019)

work page 2019
[12]

T. R. Bromley, J. M. Arrazola, S. Jahangiri, J. Izaac, N. Quesada, A. D. Gran, M. Schuld, J. Swinarton, Z. Zabaneh, and N. Killoran, Applications of near-term photonic quantum computers: software and algorithms, Quantum Science and Technology5, 034010 (2020)

work page 2020
[13]

R. F. Werner, Quantum states with einstein-podolsky- rosen correlations admitting a hidden-variable model, Phys. Rev. A40, 4277 (1989)

work page 1989
[14]

Mišta, R

L. Mišta, R. Filip, and J. Fiurášek, Continuous-variable werner state: Separability, nonlocality, squeezing, and teleportation, Phys. Rev. A65, 062315 (2002)

work page 2002
[15]

Hastrup and U

J. Hastrup and U. L. Andersen, All-optical cat-code quantum error correction, Phys. Rev. Res. 4, 043065 (2022)

work page 2022
[16]

Hastrup and U

J. Hastrup and U. L. Andersen, Protocol for generating optical gottesman-kitaev-preskill states with cavity qed, Phys. Rev. Lett.128, 170503 (2022)

work page 2022
[17]

S. L. Braunstein and H. J. Kimble, Teleportation of continuous quantum variables, Phys. Rev. Lett.80, 869 (1998)

work page 1998
[18]

B.-H. Wu, Z. Zhang, and Q. Zhuang, Continuous-variable quantum repeaters based on bosonic error-correction and teleportation: architecture and applications, Quantum Science and Technology7, 025018 (2022)

work page 2022
[19]

K. Noh, S. M. Girvin, and L. Jiang, Encoding an oscilla- tor into many oscillators, Phys. Rev. Lett.125, 080503 (2020)

work page 2020
[20]

Horodecki, P

M. Horodecki, P. Horodecki, and R. Horodecki, Separa- bilityofmixedstates: necessaryandsufficientconditions, Physics Letters A223, 1 (1996)

work page 1996
[21]

S. L. Braunstein and H. J. Kimble, Dense coding for con- tinuous variables, Phys. Rev. A61, 042302 (2000)

work page 2000
[22]

Devetak and P

I. Devetak and P. W. Shor, The capacity of a quantum channel for simultaneous transmission of classical and quantum information, Commun. Math. Phys.256, 287 (2005)

work page 2005
[23]

T. S. Cubitt, M. B. Ruskai, and G. Smith, The struc- ture of degradable quantum channels, J. Math. Phys.49, 102104 (2008)

work page 2008
[24]

M. M. Wilde,Quantum Information Theory (Cambridge University Press, 2013)

work page 2013
[25]

Pirandola, R

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communica- tions, Nat. Commun.8, 15043 (2017)

work page 2017
[26]

K. P. Seshadreesan, H. Krovi, and S. Guha, Continuous- variableentanglementdistillationoverapurelosschannel with multiple quantum scissors, Physical Review A100, 10.1103/physreva.100.022315 (2019)

work page doi:10.1103/physreva.100.022315 2019
[27]

High Fidelity Artificial Quantum Thermal State Generation using Encoded Coherent States

H. Weinstein, B. Avritzer, T. A. Brun, and J. L. Habif, High fidelity artificial quantum thermal state generation using encoded coherent states (2024), arXiv:2405.03881 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2024
[28]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, Translation of quantum states by four-wave mixing in fibers, Opt. Express13, 9131 (2005). 9 Alice Bob Eve |𝜓௖௔௧⟩ T=.1 𝑀௉ 𝑀௑ 𝐷(−𝑃) 𝐷(𝑋) |𝜓்ெௌ௏⟩ Alice Bob Eve T=.1 𝐷(𝛼) |𝜓்ெௌ௏⟩ T=.1 𝑀஻௘௟௟ FIG. 7: The circuits for continuous variable teleportation (top) and superdense coding (bottom) under the wiret...

work page 2005

[1] [1]

Inthatwork, itwasdemonstratedthatcoherentstate teleportation could be performed with an asymptotic (in r) average fidelity of1 − p, which for p <

State Teleportation In the case of TMSV state transmission, the channel above is explicitly given by ξp(ρTMSV) = pρth ⊗ ρth + (1 − p)ρTMSV, (11) which is a sort of continuous variable analog of the Werner channel [8], and has been studied previously in [9]. Inthatwork, itwasdemonstratedthatcoherentstate teleportation could be performed with an asymptotic ...

work page

[2] [2]

Superdense Coding There are some other common tasks which make use of entanglement for purposes of communication, such as superdense coding. It should be noted that continu- ous variable superdense coding via sending TMSV states through the monitored channel is not a task which can be performed steganographically, even in principle (at least with a perfec...

work page

[3] [3]

D(x p 2) |0Evei | Evei Alice Bob Eve T=.1 Expectations of Paulis Pauli Noiseless Rotated W+R (.1) W+R (.01) XX 0.9928 0.6320 0.3238 0.6189 XZ 0.0239 0.6624 0.3396 0.6692 ZX -0.0147 -0.6002 -0.3100 -0.5744 ZZ 0.9893 0.6570 0.3458 0.6557 S 1.991 2.551 1.319 2.518 FIG. 5: Using the StrawberryFields package, we were able to simulate the results of two-qubit q...

work page

[4] [4]

This is intuitive: you can imagine that Bob no longer has a communication advantage against Eve, and therefore there cannot be a quantum advantage either

State Teleportation Ifwereexaminethecatstateteleportationprotocol, we see in Figure 4 that atη = .5 there is no longer negativity to be observed. This is intuitive: you can imagine that Bob no longer has a communication advantage against Eve, and therefore there cannot be a quantum advantage either. To formalize this argument, we can examine the notion of...

work page

[5] [5]

Superdense Coding Figure 7 shows that steganographic superdense cod- ing is impossible under this eavesdropper model, since you must always send correlated information through the channel which Eve can store and detect using a joint measurement. This is in contrast to the Werner channel; while in theory Eve could hold a state in that channel as well, Alic...

work page

[6] [6]

Avritzer and T

B. Avritzer and T. A. Brun, Quantum steganography via coherent- and fock-state encoding in an optical medium, Phys. Rev. A109, 032401 (2024)

work page 2024

[7] [7]

B. B. Wu and E. E. Narimanov, A method for secure communications over a public fiber-optical network, Opt. Express 14, 3738 (2006)

work page 2006

[8] [8]

B. Wu, Z. Wang, Y. Tian, M. P. Fok, B. J. Shastri, D. R. Kanoff, and P. R. Prucnal, Optical steganography based on amplified spontaneous emission noise, Opt. Express 21, 2065 (2013)

work page 2065

[9] [9]

A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussenzveig, and M. Lipson, On-chip optical squeez- ing, Phys. Rev. Applied3, 044005 (2015)

work page 2015

[10] [10]

C. A. Fuchs and J. van de Graaf, Cryptographic distin- guishability measures for quantum mechanical states, "" (1997), arXiv:quant-ph/9712042

work page internal anchor Pith review Pith/arXiv arXiv 1997

[11] [11]

Killoran, J

N. Killoran, J. Izaac, N. Quesada, V. Bergholm, M. Amy, and C. Weedbrook, Strawberry Fields: A Software Plat- form for Photonic Quantum Computing, Quantum3, 129 (2019)

work page 2019

[12] [12]

T. R. Bromley, J. M. Arrazola, S. Jahangiri, J. Izaac, N. Quesada, A. D. Gran, M. Schuld, J. Swinarton, Z. Zabaneh, and N. Killoran, Applications of near-term photonic quantum computers: software and algorithms, Quantum Science and Technology5, 034010 (2020)

work page 2020

[13] [13]

R. F. Werner, Quantum states with einstein-podolsky- rosen correlations admitting a hidden-variable model, Phys. Rev. A40, 4277 (1989)

work page 1989

[14] [14]

Mišta, R

L. Mišta, R. Filip, and J. Fiurášek, Continuous-variable werner state: Separability, nonlocality, squeezing, and teleportation, Phys. Rev. A65, 062315 (2002)

work page 2002

[15] [15]

Hastrup and U

J. Hastrup and U. L. Andersen, All-optical cat-code quantum error correction, Phys. Rev. Res. 4, 043065 (2022)

work page 2022

[16] [16]

Hastrup and U

J. Hastrup and U. L. Andersen, Protocol for generating optical gottesman-kitaev-preskill states with cavity qed, Phys. Rev. Lett.128, 170503 (2022)

work page 2022

[17] [17]

S. L. Braunstein and H. J. Kimble, Teleportation of continuous quantum variables, Phys. Rev. Lett.80, 869 (1998)

work page 1998

[18] [18]

B.-H. Wu, Z. Zhang, and Q. Zhuang, Continuous-variable quantum repeaters based on bosonic error-correction and teleportation: architecture and applications, Quantum Science and Technology7, 025018 (2022)

work page 2022

[19] [19]

K. Noh, S. M. Girvin, and L. Jiang, Encoding an oscilla- tor into many oscillators, Phys. Rev. Lett.125, 080503 (2020)

work page 2020

[20] [20]

Horodecki, P

M. Horodecki, P. Horodecki, and R. Horodecki, Separa- bilityofmixedstates: necessaryandsufficientconditions, Physics Letters A223, 1 (1996)

work page 1996

[21] [21]

S. L. Braunstein and H. J. Kimble, Dense coding for con- tinuous variables, Phys. Rev. A61, 042302 (2000)

work page 2000

[22] [22]

Devetak and P

I. Devetak and P. W. Shor, The capacity of a quantum channel for simultaneous transmission of classical and quantum information, Commun. Math. Phys.256, 287 (2005)

work page 2005

[23] [23]

T. S. Cubitt, M. B. Ruskai, and G. Smith, The struc- ture of degradable quantum channels, J. Math. Phys.49, 102104 (2008)

work page 2008

[24] [24]

M. M. Wilde,Quantum Information Theory (Cambridge University Press, 2013)

work page 2013

[25] [25]

Pirandola, R

S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communica- tions, Nat. Commun.8, 15043 (2017)

work page 2017

[26] [26]

K. P. Seshadreesan, H. Krovi, and S. Guha, Continuous- variableentanglementdistillationoverapurelosschannel with multiple quantum scissors, Physical Review A100, 10.1103/physreva.100.022315 (2019)

work page doi:10.1103/physreva.100.022315 2019

[27] [27]

High Fidelity Artificial Quantum Thermal State Generation using Encoded Coherent States

H. Weinstein, B. Avritzer, T. A. Brun, and J. L. Habif, High fidelity artificial quantum thermal state generation using encoded coherent states (2024), arXiv:2405.03881 [quant-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2024

[28] [28]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, Translation of quantum states by four-wave mixing in fibers, Opt. Express13, 9131 (2005). 9 Alice Bob Eve |𝜓௖௔௧⟩ T=.1 𝑀௉ 𝑀௑ 𝐷(−𝑃) 𝐷(𝑋) |𝜓்ெௌ௏⟩ Alice Bob Eve T=.1 𝐷(𝛼) |𝜓்ெௌ௏⟩ T=.1 𝑀஻௘௟௟ FIG. 7: The circuits for continuous variable teleportation (top) and superdense coding (bottom) under the wiret...

work page 2005