Probabilistic Quantum Gates between Remote Atoms through Interference of Optical Frequency Qubits

C. Monroe; D. L. Moehring; L.-M. Duan; M. J. Madsen; P. Maunz; R. N. Kohn Jr.

REVIEW

Probabilistic Quantum Gates between Remote Atoms through Interference of Optical Frequency Qubits

L.-M. Duan, M. J. Madsen, D. L. Moehring, P. Maunz, R. N. Kohn Jr., C. Monroe

Quantum Physics · Submitted 31 Mar 2006 · 20 references

Pith's verdict: Smart proposal with a clean measurement-gate derivation, but the π-decay assumption is physically wrong for alkali-like atoms—needs frequency-filtering analysis.

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arXiv IDquant-ph/0603285 (version 1)

Pith IDSMYAR45E, Pith's permanent record of this paper and its review

CitationC. Monroe, D. L. Moehring, L.-M. Duan, M. J. Madsen, P. Maunz, R. N. Kohn Jr.. "Probabilistic Quantum Gates between Remote Atoms through Interference of Optical Frequency Qubits." arXiv:quant-ph/0603285 (2006). https://pith.science/paper/SMYAR45E

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Claim paper

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Editor's note

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Colleague,

The core idea here is genuinely nice: encode the atomic qubit in two hyperfine clock states, excite with a broadband π pulse, and let each state emit a photon whose frequency tags which ground state it came from. Interfering two such photons on a beamsplitter and looking for coincidences projects the atoms onto the Z1Z2 = -1 eigenspace. The derivation of Eq. (2) is correct under the two-mode idealization, and the claimed robustness to atomic motion and interferometer phase noise is real, because both frequency components pick up the same spatial phase. This is a clever extension of the Barrett-Kok / Duan-Raussendorf measurement-gate program, and the fact that it works outside the Lamb-Dicke regime is a practical point worth having.

The problem is the physical assumption behind Eq. (1). The paper says the two excited hyperfine levels can only decay back to their originating qubit states via π photons. For any real alkali-like atom that's not true. For 111Cd+ with F=0 and F=1 ground states, the level reached from |0> (F'=1,m=0) can also decay via a π photon to |1> (F=1,m=0). That decay produces a third photon frequency and leaves the atom in the wrong qubit state. If you don't filter that frequency out, a coincidence can be heralded by an atom that started in |0> but ended in |1>, so the conditional atomic state is not the projection of Eq. (2). If you do filter it, the success probability is lower than the claimed ps, because η_b has to be the branching ratio into the two desired frequency modes, not the total π branching. The manuscript never analyzes this channel. Footnote 19 only discusses bit-flip errors on gate failure, not errors within the success heralds.

This is a load-bearing flaw in the sense that Eq. (1)'s correlation is the whole basis of the gate. But it's a fixable one: add frequency filtering (or choose a species/level scheme where the unwanted decay is absent), and redo the success probability with the correct branching ratios. The cluster-state scaling argument, which is borrowed from Duan-Raussendorf, is fine once you accept the gate model.

The paper is worth a serious referee: the idea is original, the ideal derivation is clean, and the oversight is exactly the kind a good referee should catch. I'd send it to review and ask for the decay-channel analysis.

Referee report

Significance

The central idea—using frequency-encoded optical qubits to realize a heralded remote ZZ measurement in free space—is attractive and, if it worked, would be significant: it would remove the Lamb-Dicke requirement, avoid strict interferometric phase stability, and connect naturally to a known scalable framework. The paper also contains genuine strengths: a clean derivation of the ideal projection in Eq. (2), a closed-form success probability, and a careful discussion of Doppler and phase-noise robustness, along with an explicit reduction of the scalability argument to Ref. [6]. However, the physical validity of the central derivation depends entirely on the selection-rule claim in the paragraph following Fig. 1, and that claim is incorrect for the very species cited, 111Cd+. The core gate therefore is not realized as described, and the predicted fidelity and success probability are not supported for realistic alkali-like atoms.

Major objections (3)

[Paragraph following Fig. 1; Eq. (1)] The assertion that the excited P1/2 levels 'can only decay back to the ground states |F,m=0> and |F+1,m=0>, respectively' is incorrect for alkali-like atoms. For the F=0 case of 111Cd+ used in the text, the level P1/2 (F'=1,m=0) reached from |0> can π-decay to both S1/2 (F=0,m=0) and S1/2 (F=1,m=0), the latter being |1>. The level P1/2 (F'=0,m=0) reached from |1> can π-decay to |1>. Hence the emitted photon spectrum contains at least three frequency components, and the excitation-decay state is not Eq. (1). The preceding selection-rule claim is also too strong: ΔF=0 electric dipole transitions are allowed, so the ultrafast pulse can excite |1> to F'=1 in addition to F'=0. This is a load-bearing error for the entire gate derivation.
[Eq. (2) and the paragraph defining the ZZ measurement gate] Because of the extra decay channel, the coincidence measurement does not implement the claimed ZZ measurement. As a concrete counterexample, prepare both atoms in |0>; after excitation-decay, a detected ν0/ν1 pair can arise from one atom emitting ν0 and the other emitting ν1, yielding an atomic state in the odd-parity subspace (|01>-|10> up to normalization). For initial |01>, the same detection pattern yields |01> up to a factor. Thus the map on the computational basis is not proportional to Z1(I-Z1Z2): the |00> component does not stay in the even-parity subspace, and the output depends on the branching amplitudes in a way that cannot be removed by local rotations. Eq. (2) therefore misstates the postselected atomic state for general inputs.
[Success probability ps and footnote [19]] The expression ps = η_d² η_c² η_b²/4 is invalid in the presence of the extra channel. The branching fraction η_b is not a single number for the two qubit states: the π-decay probabilities from the two excited hyperfine levels to the desired ground states differ, and the undesired π channel can be confused with the desired frequency mode. The coincidence probability becomes initial-state dependent, so an 'overall' success probability cannot be defined without specifying an ensemble. Frequency filtering of the unwanted channel would reduce the collection efficiency below η_c, so the claimed scaling of the gate efficiency does not follow. Footnote [19] addresses bit-flip errors only in failed runs and does not repair the fidelity of the heralded success events, which is the central claim.

Minor objections (3)

[Scalability paragraph after the ZZ measurement gate] The recursion formula for cluster-state growth is only sketched; the modified critical length nc = 1 + 4(1-ps)/ps should be derived explicitly from the failure model described in footnote [19] before the claimed scaling is accepted, since footnote [19] states that the destroyed-qubit model differs from that of Ref. [7].
[Footnote [19]] There are several typographical errors in footnote [19] ('π-decaly', 'alwyas', 'contruction', 'scalalbility') that should be corrected.
[Fig. 2] The label 'DD' in Fig. 2 is unexplained; the caption should define all abbreviations used in the figure.

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The paper

The paper claims

Interfering frequency-encoded photons from two atoms yields a heralded entangling measurement gate, robust to atomic motion and interferometer phase noise.

The reading

The paper proposes a scheme to perform a probabilistic entangling gate on two atoms in remote traps, using the interference of spontaneously emitted photons whose frequency encodes the atomic qubit state. Each atom is excited with an ultrafast π-polarized pulse, and the π-polarized decay photon carries the qubit in its frequency ($\nu_0$ or $\nu_1$), producing the atom-photon entangled state of Eq. (1). When one photon from each atom is collected and detected in coincidence after a beam splitter, the two atoms are projected onto the $Z_1Z_2=-1$ eigenspace, giving the entangled state of Eq. (2) with success probability $p_s = \eta_d^2 \eta_c^2 \eta_b^2 / 4$. The gate does not require cooling to the Lamb-Dicke limit and is insensitive to interferometer phase noise. Because probabilistic gates are sufficient for scalable cluster-state quantum computation, this offers a practical route to remote entanglement with trapped ions or neutral atoms.

What carries the argument

The central object is the optical frequency qubit: a photonic qubit encoded in two frequency modes $\nu_0$ and $\nu_1$ with the same polarization, created by the ultrafast π-polarized excitation and the subsequent π-polarized spontaneous decay. The selection rules map each atomic qubit state $|0\rangle$ and $|1\rangle$ to a distinct excited hyperfine level, so the decay photon frequency is perfectly correlated with the initial qubit state, yielding the atom–photon state $|\Psi_{ap}\rangle = c_0|0\rangle|\nu_0\rangle + c_1|1\rangle|\nu_1\rangle$. The beam splitter interference of two such photons, followed by coincidence detection, erases the which-atom information and projects the atoms onto the anti-symmetric photonic state, which is the $Z_1Z_2$ measurement. The same polarization and near-degenerate frequencies of the two components are what make the scheme robust to atomic motion and optical path fluctuations.

Extended reading notes

Core claim

The central claim is that a coincident detection of two photons, one from each atom after interference at a beam splitter, implements a quantum non-demolition measurement of the operator $Z_1Z_2$ on the two atomic qubits. Before detection, each atom–photon system is in the entangled state $|\Psi_{ap}\rangle_i = c_0 |0\rangle_i |\nu_0\rangle_i + c_1 |1\rangle_i |\nu_1\rangle_i$. The coincidence measurement selects the anti-symmetric two-photon component $|\Phi_{AS}\rangle = (|\nu_0\rangle_1 |\nu_1\rangle_2 - |\nu_1\rangle_1 |\nu_0\rangle_2)/\sqrt{2}$, projecting the atoms into the state $|\Psi_{12}\rangle \propto c_0 d_1 |0\rangle_1 |1\rangle_2 - c_1 d_0 |1\rangle_1 |0\rangle_2$, which is the $Z_1Z_2 = -1$ eigenspace up to a single-qubit rotation. The success probability is $p_s = \eta_d^2 \eta_c^2 \eta_b^2/4$, where $\eta_d$, $\eta_c$, and $\eta_b$ are the detector efficiency, photon collection efficiency, and branching ratio into the π-decay channel. Because both frequency components acquire the same random phase from atomic position and the same interferometric phase noise, the gate is robust to atomic motion beyond the Lamb-Dicke limit and to interferometer instabilities. The paper also argues that such a probabilistic measurement gate can be used to build 2D cluster states, making it a resource for scalable quantum computation.

Load-bearing premise

The scheme assumes that after the π-polarized excitation each excited hyperfine level decays only back to the originating qubit ground state via a π-polarized photon, whereas real alkali-like atoms also allow decay from the excited level reached by $|0\rangle$ to $|1\rangle$, adding a third photon frequency and bit-flip errors to the heralded gate.

Editorial extensions

If this is right

The gate succeeds with probability $p_s = \eta_d^2 \eta_c^2 \eta_b^2/4$; increasing the collection solid angle or adding optical cavities is the main route to higher success rates.
The scheme works for any alkali-like atom or ion with hyperfine ground states, including $^{111}$Cd$^+$, and does not require Lamb-Dicke localization, simplifying traps with high heating rates.
Because the operation is a $Z_1Z_2$ measurement, it can serve as the entangling primitive for constructing 2D cluster states, with resource overhead scaling polynomially with $1/p_s$ and system size.
The gate is insensitive to interferometer phase drift and birefringence because both frequency components share the same polarization and are close in frequency.
If the gate fails, the atomic qubits are destroyed (with possible bit-flip errors from the π-decay channels), matching the noise model under which scalability was proven in Ref. [6].

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same frequency-encoding idea could be extended to a full Bell measurement by resolving the frequency modes before the beam splitter, which would allow deterministic entanglement swapping; the paper only analyzes the $Z_1Z_2$ coincidence measurement.
The predicted gate fidelity depends on the assumption that each excited hyperfine level decays only to its originating ground state. A direct measurement of the π-polarized emission spectrum would reveal a third frequency component if this assumption fails, and the fidelity of the heralded state would drop accordingly.
The robustness to atomic motion suggests the scheme could be applied to neutral atoms in shallow optical traps or to ions in chip traps with elevated heating, as long as the Doppler shift stays small compared to the pulse bandwidth.
The gate's reliance on frequency rather than polarization implies that spectral filtering or cavity enhancement could boost the collection efficiency without compromising the qubit encoding, a path the paper mentions but does not quantify.

Original abstract

We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.69 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.11 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.

background contribution method result interpretation main claim

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits.	contribution 0.99	0.28	0.38	hedged possibility 0.45
s1	The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities.	contribution 0.46	0.40	0.15	asserted 1.00
s2	Such probabilistic gates can be used for scalable quantum computation.	interpretation 0.97	0.10	0.26	hedged possibility 0.72

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from argument 0.81.

What was examined, and what was not

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full text
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: The atomic level configuration and the laser excita

**Figure 2.** FIG. 2: The ZZ measurement gate on the atoms i and j. The

Figures reproduced from arXiv:quant-ph/0603285 by the authors.

References

Works cited (20)

[19]

Note, however, that the noise model assumed in Ref. [7] is more restrictive. It assumes there that if a gate fails, states of the two target qubits are not destroyed, but in- stead, they are subject only to Z type of errors (without bit ﬂips from |0⟩ to |1⟩, for instance). In our physical im- plementation, however, due to the existence of π -decaly channe...

View on Pith
[6]

L.-M. Duan and R. Raussendorf, Phys. Rev. Lett. 95, 080503 (2005)

View on Pith 2005
[1]

L. M. Duan, M. D. Lukin, J. I. Cirac, P,. Zoller, Nature 414, 413 (2001)

View on Pith 2001
[2]

E. Knill, R. Laﬂamme, and G. Milburn, Nature 409, 46 (2001)

View on Pith 2001
[3]

A. Kuzmich, et al. , Nature 423, 731 (2003); C. H. van der Wal et al. , Science 301, 196 (2003)

View on Pith 2003
[4]

B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe, Nature 428, 153-157 (2004)

View on Pith 2004
[5]

D. L. Moehring, M. J. Madsen, B. B. Blinov, and C. Monroe, Phys. Rev. Lett. 93, 090410 (2004)

View on Pith 2004
[7]

S. D. Barrett, P. Kok, Phys. Rev. A 71, 060310(R) (2005)

View on Pith 2005
[8]

L.-M. Duan, B. Wang, J. Kimble, Phys. Rev. A 72, 4 022320 (2005)

View on Pith 2005
[9]

Y. L. Lim et al., Phys. Rev. A 73, 012304 (2006); Y. L. Lim, A. Beige, L. C. Kwek, Phys. Rev. Lett. 95, 030505 (2005)

View on Pith 2006
[10]

M. J. Madsen et al., quant-ph/0603258

View on Pith Pith review arXiv
[11]

D. Stick et al., Nature Physics 2, 36 (2006); D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002)

View on Pith 2006
[12]

S. Seidelin, et al., quant-ph/0601173 (2006)

View on Pith Pith review arXiv 2006
[13]

L. Deslauriers, et al., quant-ph/0602003 (2006)

View on Pith Pith review arXiv 2006
[14]

If an ultrafast laser pulse is not available, one can re- place it by two phase-locked narrow-band pulses which drives the D1 transitions |F, m = 0⟩ → | F ′ + 1, m = 0⟩ and |F + 1, m = 0⟩ → | F ′, m = 0⟩ (F ′ = F ), respec- tively

View on Pith
[15]

For 111Cd+ (or for any atoms with the nuclear spin I = 1 / 2), one can also drive the D2 line S1/ 2 → P3/ 2, where the two corresponding hyperﬁne transitions are given by |F, m = 0⟩ → |F ′, m = 0⟩ and |F + 1, m = 0⟩ → |F ′ + 1, m = 0⟩ with F ′ = F + 1, see Ref. [10]

View on Pith
[16]

For instance, for 133Cs atoms or 111Cd+ ions, the hyper- ﬁne splitting is about 9 GHz (14 GHz), while the natural linewidth of the excited level (the inverse of the lifetime) is around 5 MHz (60 MHz). In both cases, the condition is well satisﬁed

View on Pith
[17]

L.-M. Duan, B. B. Blinov, D. L. Moehring, C. Monroe, Quant. Inf. Comp. 4, 165-173 (2004)

View on Pith 2004
[18]

J. McKeever, J. R. Buck, A. D. Boozer, and H. J. Kimble, Phys. Rev. Lett. 92, 143601 (2004); P. Maunz, et al., Nature 428, 50 (2004); J. A. Sauer, et al., Phys. Rev. A69, 051804 (2004); G. Guthorlein, et al.,Nature 414, 49 (2001); A. Mundt, et al., Phys. Rev. Lett. 89, 103001 (2002)

View on Pith 2004
[20]

H.J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001); R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

View on Pith 2001

How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [19]

Note, however, that the noise model assumed in Ref. [7] is more restrictive. It assumes there that if a gate fails, states of the two target qubits are not destroyed, but in- stead, they are subject only to Z type of errors (without bit ﬂips from |0⟩ to |1⟩, for instance). In our physical im- plementation, however, due to the existence of π -decaly channe...

View on Pith

[2] [6]

L.-M. Duan and R. Raussendorf, Phys. Rev. Lett. 95, 080503 (2005)

View on Pith 2005

[3] [1]

L. M. Duan, M. D. Lukin, J. I. Cirac, P,. Zoller, Nature 414, 413 (2001)

View on Pith 2001

[4] [2]

E. Knill, R. Laﬂamme, and G. Milburn, Nature 409, 46 (2001)

View on Pith 2001

[5] [3]

A. Kuzmich, et al. , Nature 423, 731 (2003); C. H. van der Wal et al. , Science 301, 196 (2003)

View on Pith 2003

[6] [4]

B. B. Blinov, D. L. Moehring, L.-M. Duan, C. Monroe, Nature 428, 153-157 (2004)

View on Pith 2004

[7] [5]

D. L. Moehring, M. J. Madsen, B. B. Blinov, and C. Monroe, Phys. Rev. Lett. 93, 090410 (2004)

View on Pith 2004

[8] [7]

S. D. Barrett, P. Kok, Phys. Rev. A 71, 060310(R) (2005)

View on Pith 2005

[9] [8]

L.-M. Duan, B. Wang, J. Kimble, Phys. Rev. A 72, 4 022320 (2005)

View on Pith 2005

[10] [9]

Y. L. Lim et al., Phys. Rev. A 73, 012304 (2006); Y. L. Lim, A. Beige, L. C. Kwek, Phys. Rev. Lett. 95, 030505 (2005)

View on Pith 2006

[11] [10]

M. J. Madsen et al., quant-ph/0603258

View on Pith Pith review arXiv

[12] [11]

D. Stick et al., Nature Physics 2, 36 (2006); D. Kielpinski, C. Monroe, and D. J. Wineland, Nature 417, 709 (2002)

View on Pith 2006

[13] [12]

S. Seidelin, et al., quant-ph/0601173 (2006)

View on Pith Pith review arXiv 2006

[14] [13]

L. Deslauriers, et al., quant-ph/0602003 (2006)

View on Pith Pith review arXiv 2006

[15] [14]

If an ultrafast laser pulse is not available, one can re- place it by two phase-locked narrow-band pulses which drives the D1 transitions |F, m = 0⟩ → | F ′ + 1, m = 0⟩ and |F + 1, m = 0⟩ → | F ′, m = 0⟩ (F ′ = F ), respec- tively

View on Pith

[16] [15]

For 111Cd+ (or for any atoms with the nuclear spin I = 1 / 2), one can also drive the D2 line S1/ 2 → P3/ 2, where the two corresponding hyperﬁne transitions are given by |F, m = 0⟩ → |F ′, m = 0⟩ and |F + 1, m = 0⟩ → |F ′ + 1, m = 0⟩ with F ′ = F + 1, see Ref. [10]

View on Pith

[17] [16]

For instance, for 133Cs atoms or 111Cd+ ions, the hyper- ﬁne splitting is about 9 GHz (14 GHz), while the natural linewidth of the excited level (the inverse of the lifetime) is around 5 MHz (60 MHz). In both cases, the condition is well satisﬁed

View on Pith

[18] [17]

L.-M. Duan, B. B. Blinov, D. L. Moehring, C. Monroe, Quant. Inf. Comp. 4, 165-173 (2004)

View on Pith 2004

[19] [18]

J. McKeever, J. R. Buck, A. D. Boozer, and H. J. Kimble, Phys. Rev. Lett. 92, 143601 (2004); P. Maunz, et al., Nature 428, 50 (2004); J. A. Sauer, et al., Phys. Rev. A69, 051804 (2004); G. Guthorlein, et al.,Nature 414, 49 (2001); A. Mundt, et al., Phys. Rev. Lett. 89, 103001 (2002)

View on Pith 2004

[20] [20]

H.J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001); R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)

View on Pith 2001