arxiv: 2605.11457 · v1 · submitted 2026-05-12 · 🪐 quant-ph

Recognition: no theorem link

Loss-induced quantum nonreciprocity and entanglement in superconducting qubits

Yu-Meng Ren , Peng-Bo Li

Authors on Pith no claims yet

Pith reviewed 2026-05-13 02:17 UTC · model grok-4.3

classification 🪐 quant-ph

keywords loss-induced nonreciprocitynonreciprocal entanglementsuperconducting qubitstransmon qubitslossy cavitiesquantum networksdirection-dependent interference

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The pith

Loss in auxiliary cavities can induce nonreciprocal coupling and entanglement between two remote superconducting qubits through direction-dependent interference.

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

The paper proposes a scheme in which engineered loss in two auxiliary cavities generates nonreciprocal interactions between distant transmon qubits. Coherent phases from the qubit-cavity couplings reverse upon direction reversal, while loss-induced phases stay fixed, producing unequal interference conditions and therefore unequal effective couplings in opposite directions. This mechanism turns loss into a controllable resource that produces nonreciprocal quantum entanglement whose strength and character can be tuned by the relative loss phase. The approach directly links engineered dissipation to directional entanglement, offering a route toward scalable quantum networks that do not require perfect isolation from the environment.

Core claim

We show that loss can be used as a resource to generate nonreciprocity and nonreciprocal entanglement in a superconducting platform consisting of two remote transmon qubits linked by two lossy auxiliary cavities. The nonreciprocity arises from interference among multiple lossy coupling paths: coherent phases associated with the qubit-resonator couplings reverse sign under propagation reversal, while loss-induced phases remain direction-independent. Their combined effect produces different interference conditions in the two directions, resulting in unequal effective couplings. The resulting nonreciprocal entanglement is tunable by the relative phase induced by loss, allowing both reciprocal (

What carries the argument

Interference between multiple lossy coupling paths in which coherent qubit-resonator phases reverse sign under direction reversal while loss phases remain direction-independent.

If this is right

Nonreciprocal entanglement becomes possible without external magnetic fields or active modulation.
The loss phase provides a tunable knob that can switch the system between reciprocal and nonreciprocal regimes.
The scheme supplies a concrete mechanism for realizing nonreciprocal quantum gates or channels in circuit-QED networks.
Engineered loss can be repurposed as a design element rather than a defect to be minimized.

Where Pith is reading between the lines

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

The same interference principle could be tested in other bosonic platforms such as optomechanical or magnonic systems where loss is similarly unavoidable.
Scaling to many qubits might allow construction of nonreciprocal quantum routers or directed entanglement distribution without additional hardware.
The method suggests a general design rule: pair coherent couplings with direction-independent dissipative paths to break reciprocity at the quantum level.

Load-bearing premise

Coherent phases from the qubit-resonator couplings change sign when propagation direction reverses, whereas phases arising from loss stay the same in both directions.

What would settle it

Measuring equal transmission amplitudes or identical entanglement measures when the two qubits exchange roles would falsify the claim; observing direction-dependent differences in coupling strength or entanglement would support it.

Figures

Figures reproduced from arXiv: 2605.11457 by Peng-Bo Li, Yu-Meng Ren.

**Figure 2.** Figure 2: FIG. 2. (a) Contour maps of the isolation factor [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Population dynamics for each qubit under different initial conditions and detuning configurations. (a)-(d) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Time evolution of concurrence between two qubits under [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Dynamics of qubit populations and concurrence with and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Dynamics of qubit populations with different qubit detunings in complete isolation condition. (a)-(d) Time evolution of qubit popula [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

read the original abstract

Losses are ubiquitous in physics and are usually regarded as harmful in quantum information processing. Here, we propose a loss-induced scheme to achieve nonreciprocity and nonreciprocal entanglement in a superconducting platform, where two remote superconducting transmon qubits are connected via two lossy auxiliary cavities. The nonreciprocity in our scheme originates from interference between multiple lossy coupling paths. The coherent phases associated with the qubit-resonator couplings reverse sign under propagation reversal, while the loss-induced phases remain direction independent. Their combined effect leads to different interference conditions in the opposite directions, resulting in unequal effective couplings. We show that this loss-induced scheme can generate nonreciprocal quantum entanglement, indicating that loss can be utilized as a resource. Moreover, the tunability of nonreciprocity and nonreciprocal entanglement in our scheme can be manipulated by the relative phase induced by loss, allowing to tailor both reciprocal and nonreciprocal behaviors. Our results establish a direct link between engineered loss and nonreciprocal entanglement in quantum information processing and offer potential applications in scalable quantum networks.

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 gives a workable interference scheme to turn loss into tunable nonreciprocity and nonreciprocal entanglement between two transmons, but the central phase-separation claim needs explicit confirmation in the effective Hamiltonian.

read the letter

Hi, the main thing to know is that this work proposes using two lossy auxiliary cavities to connect remote transmon qubits and generate direction-dependent effective couplings through interference. Coherent phases reverse with propagation direction while loss phases stay fixed, producing unequal forward and backward couplings that can also yield nonreciprocal entanglement. The relative loss phase then tunes the strength of the asymmetry, including the option to recover reciprocal behavior. That tunability and the direct link to entanglement are the concrete advances here, and they sit on a standard superconducting platform that makes the idea testable in existing hardware. The qualitative picture is laid out clearly and the applications to directional quantum networks are spelled out without overclaiming. The derivations appear to follow ordinary interference and adiabatic elimination steps, with no obvious circularity or invented parameters. The soft spot is exactly the one the stress test flags: once the cavities are eliminated, standard Lindblad or complex-frequency treatments can add direction-dependent contributions from cavity susceptibility or input-output relations. The paper must show the explicit effective coupling expression to confirm the claimed asymmetry survives without cancellation or extra terms. If that derivation is there and clean, the argument holds; if it is only sketched, the claim stays provisional. This is the sort of proposal that would interest people working on loss engineering and nonreciprocal circuit QED. A reader focused on quantum networks or passive directional devices would find the scheme and the tunability discussion useful. It deserves peer review because the platform is practical and the core mechanism is falsifiable with standard tools, even if the effective-model details may need tightening in revision.

Referee Report

1 major / 1 minor

Summary. The paper proposes a scheme in which two remote transmon qubits are coupled through two lossy auxiliary cavities to realize loss-induced nonreciprocity and nonreciprocal entanglement. Nonreciprocity is attributed to interference among multiple lossy paths: coherent qubit-resonator phases reverse sign upon propagation reversal while loss-induced phases remain direction-independent, producing unequal effective couplings in opposite directions. The relative phase induced by loss is claimed to tune both the degree of nonreciprocity and the generation of nonreciprocal entanglement, positioning loss as a controllable resource for quantum networks.

Significance. If the phase-separation mechanism and resulting effective couplings can be rigorously derived and verified, the work would establish a concrete route to harness engineered loss for tunable nonreciprocity and entanglement in superconducting circuits, with potential utility for directional quantum communication and scalable networks.

major comments (1)

[Main text (interference mechanism)] The central interference argument (main text following the abstract) asserts that loss-induced phases are direction-independent while coherent phases reverse, yet supplies no explicit Hamiltonian, master equation, or adiabatic-elimination formula for the effective qubit-qubit coupling. Without this derivation it is impossible to confirm that the claimed phase distinction survives standard treatments of cavity loss (Lindblad operators or complex detunings) and does not acquire additional direction-dependent contributions from input-output boundary conditions or cavity susceptibility.

minor comments (1)

[Abstract] The abstract and introduction would benefit from a brief statement of the parameter regime (e.g., strong-coupling vs. bad-cavity limits, specific values of loss rates relative to couplings) in which the scheme is intended to operate.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive criticism. We have revised the manuscript to provide the requested explicit derivation of the effective qubit-qubit coupling while preserving the original claims.

read point-by-point responses

Referee: [Main text (interference mechanism)] The central interference argument (main text following the abstract) asserts that loss-induced phases are direction-independent while coherent phases reverse, yet supplies no explicit Hamiltonian, master equation, or adiabatic-elimination formula for the effective qubit-qubit coupling. Without this derivation it is impossible to confirm that the claimed phase distinction survives standard treatments of cavity loss (Lindblad operators or complex detunings) and does not acquire additional direction-dependent contributions from input-output boundary conditions or cavity susceptibility.

Authors: We agree that an explicit derivation is necessary for rigor and that its absence from the main text was a shortcoming. In the revised manuscript we have added a dedicated subsection (new Sec. II) containing: (i) the full system Hamiltonian with coherent qubit-cavity couplings g_j and cavity frequencies; (ii) the Lindblad master equation with cavity-loss operators sqrt(kappa) a_j; and (iii) the adiabatic-elimination procedure that yields the effective qubit-qubit coupling J_eff. Under the standard treatment (complex detunings Delta - i kappa/2 for lossy cavities), the loss-induced contribution to the phase is carried by the imaginary part of the cavity susceptibility and remains invariant under propagation reversal, while the coherent phase factor e^{i phi} reverses sign. Input-output boundary conditions are accounted for via the standard scattering formalism; they contribute only to the overall normalization of the effective coupling and introduce no additional direction-dependent phase in the regime kappa >> g, |Delta|. We have verified this both analytically and by direct numerical integration of the full master equation against the effective model. The revised text now makes the interference mechanism fully traceable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via standard interference assumptions

full rationale

The paper derives nonreciprocity from interference between coherent phases (reversing under propagation) and loss-induced phases (direction-independent), leading to unequal effective couplings. This follows directly from the stated model without any quoted reduction of the target result to a fitted parameter, self-defined quantity, or load-bearing self-citation chain. No equations rename inputs as predictions or smuggle ansatze via prior self-work. The central claim rests on explicit phase properties and adiabatic elimination, which are independent of the final nonreciprocity outcome. This is the expected non-circular case for a proposal paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full Hamiltonian, parameter values, and derivation steps are unavailable, so the ledger is necessarily incomplete.

free parameters (1)

relative phase induced by loss
Used to tune between reciprocal and nonreciprocal regimes; appears as an adjustable parameter in the scheme description.

axioms (1)

domain assumption Coherent phases reverse sign under propagation reversal while loss-induced phases remain direction-independent
Invoked to produce unequal interference conditions in opposite directions.

pith-pipeline@v0.9.0 · 5480 in / 1275 out tokens · 54679 ms · 2026-05-13T02:17:54.577253+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

153 extracted references · 153 canonical work pages

[1]

The con- necting modes are described by: ˆHc = P2 n=1 ω(n) c ˆc(n)†ˆc(n) withω (n) c the frequencies of the connecting modes

The setup in the laboratory frame In the laboratory frame, the Hamiltonian of the system can be written as(ℏ= 1): ˆHlab = ˆHq(t) + ˆHc + ˆHint(t).(A1) Here, the qubit Hamiltonian is ˆHq(t) = 1 2 ωm(t)ˆσz, where ωm(t)is time-dependent due to flux modulation. The con- necting modes are described by: ˆHc = P2 n=1 ω(n) c ˆc(n)†ˆc(n) withω (n) c the frequencie...

work page
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i (A5) whereδω(t) =ω m(t)−ω 0 =A 1 cos(ωd1t+ψ 1) + A2 cos(ωd2t+ψ 2)and∆ (n) 0 =ω 0 −ω (n) c is the bare de- tuning of then-th connecting mode from the rotating frame frequencyω 0

Rotating frame atω 0 We now move to the same global rotating frame used in the main text, defined by the average qubit frequencyω 0 via the unitary operator: ˆUrot(t) = exp " −iω0 1 2 ˆσz + 2X n=1 ˆc(n)†ˆc(n) ! t # .(A4) The laboratory Hamiltonian transforms as ˆHrot(t) = ˆU † rot(t) ˆHlab(t) ˆUrot(t)−i ˆU † rot(t) ˙ˆUrot, takes the form: ˆHrot(t) =1 2 δω...

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The trans- formation is given by the unitary operator ˆUm(t) = Texp h −i R t 0 δω(τ)dτ i

Removal of the qubit modulation term To expose the sideband structure induced by the qubit- frequency modulation, we remove the local qubit term with respect to the Hamiltonian 1 2 δω(t)ˆσz. The trans- formation is given by the unitary operator ˆUm(t) = Texp h −i R t 0 δω(τ)dτ i . Since[δω(t 1)ˆσz, δω(t2)ˆσz] = 0for ∀t1, t2, the time-ordering operatorTcan...

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Interaction picture with respect to the bare detuning Then we introduce an interaction picture associate with the bare connecting mode detuning: ˆU∆0(t) = exp " i 2X n=1 ∆(n) 0 ˆc(n)†ˆc(n)t # .(A8) And the corresponding Hamiltonian is transformed as: ˆHI(t) = 2X n=1 λ(n) h ˆσ+ˆc(n)eiΦ(t)ei∆(n) 0 t +H.c. i (A9) 6 Sideband selection with residual engineered...

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∞X k=−∞ Jk A1 ωd1 eik(ωd1t+ψ1) # ·

Jacobi-Anger expansion Integrating the modulation phase and substituting it into α(n)(t), we obtain: α(n)(t) =∆(n) 0 t+ A1 ωd1 sin(ωd1t+ψ 1) + A2 ωd2 sin(ωd2t+ψ 2) + const., (A10) where the constant term only contributes a global phase and can be omitted. To proceed, we apply the Jacobi-Anger expansion eizsin Θ = P k Jk(z)eikΘ, whereJ k(z)is thek-th order...

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Specifically, for each connecting mode we impose the sideband condition∆(n) 0 +kωd1+lωd2 = ∆(n) with∆ (n) the residual engineered detuning that remains after sideband selection

Sideband selection with residual engineered detunings To activate the desired couplings to the two connecting modes while retaining residual engineered detunings, the drive frequencies are chosen to compensate the bare detunings up to residual detunings. Specifically, for each connecting mode we impose the sideband condition∆(n) 0 +kωd1+lωd2 = ∆(n) with∆ ...

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Transformation to the residual engineered detuning frame Next, we absorb the phase factorse i∆(n)t in Eq. (A13) by introducing the residual engineered detuning frame: ˆUres(t) = exp " −i 2X n=1 ∆(n)ˆc(n)†ˆc(n)t # .(A15) Using ˆU † resˆc(n) ˆUres = ˆc(n)e−i∆(n)t, the slow Hamiltonian ˆHslow is transformed as ˆHeng = ˆU † res ˆHslow ˆUres −i ˆU † res ˙ˆUres...

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When each qubitQ m (m=L, R) is independently modulated by its own set of drive parameters, the slow dynam- ics is governed by the generalized Hamiltonian in Eq

Generalization to two qubits Finally, we extend the above derivation to the two qubits case. When each qubitQ m (m=L, R) is independently modulated by its own set of drive parameters, the slow dynam- ics is governed by the generalized Hamiltonian in Eq. (A16): ˆHeng =− 2X n=1 ∆(n)ˆc(n)†ˆc(n) + 2X n=1 h g(n) L ˆσ+ L +g (n) R ˆσ+ R ˆc(n) +H.c. i , (A17) TAB...

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