Quantum teleportation with partially entangled joint measurements induced by coherent errors

arXiv:2605.12130 · quant-ph · Submitted 2026-05-12 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum teleportation with partially entangled joint measurements induced by coherent errors".

Mira: Quantum teleportation performance is fundamentally limited by measurement entanglement in realistic scenarios where joint measurements are imperfect due to coherent errors.

Kai: First, who's behind it and why it matters.

Title and authors: Mira: To start, let's look at the title and authors of "Quantum teleportation with partially entangled joint measurements induced by coherent errors." The title immediately signals that the paper is tackling a problem where our usual assumption—that Bell-state measurements are perfect—is being violated by physical realities.

Kai: I agree, Mira; it tells us right away that we're dealing with realistic implementations where joint measurements aren't ideal and are getting deformed by coherent errors in entangling operations. The authors list Shin, Lee, and others, which tells us this is coming from a team deeply embedded in the experimental side of quantum hardware.

Lev: As a quantum error correction researcher, I’m interested to see what specific types of coherent errors they modeled; are we talking about simple dephasing or something more complex that affects the entanglement itself?

Mira: The paper implies they are dealing with coherent errors in entangling gates that deform the ideal Bell basis into a rotated, partially entangled measurement basis parameterized by an error strength 't'.

Kai: That parameterization is key because it gives us a way to quantify this deformation based on how long we let the system evolve under those imperfect entangling times.

Lev: If you can quantify 't' precisely, then running this on real hardware becomes much more manageable because you have a specific error metric to track instead of just saying "the gate isn't perfect."

Mira: Precisely, and they show that this deformation directly impacts the success probability through equations like F tele(t) = two + EM(t) cubed, which clearly shows a mathematical dependency on that error strength <ref:2605.12130#pg0>.

Kai: That equation is pretty telling because it proves that even if our quantum channel is perfectly entangled, the standard protocol performance degrades significantly just because of how long we entangle things.

Lev: For running this on real hardware, this means we need to characterize the time-dependent evolution of our entangling gates very carefully to determine 't' before we can even start calculating anything meaningful.

Mira: Their work also moves beyond just standard fidelity degradation and introduces a new framework for handling these partially entangled measurements by proposing a strategy using a measurement reversal framework.

Kai: That’s what really caught my eye; they aren't just describing the problem, they are actually proposing a solution to bypass the limitations imposed by those imperfect joint measurements.

Lev: A proposed solution is exciting because it suggests we can maintain unit fidelity for pure inputs even when the underlying measurement resource is weaker than ideal.

Mira: That framework allows Bob to perform a more general probabilistic reversing operation at his side, enabling him to recover the original input state based on the measurement outcome.

Kai: It sounds like they’re shifting the burden from needing perfect initial hardware to having sophisticated classical post-processing capability on the receiver's side.

Lev: If we can implement that reversal probabilistically, it means we can use less entangled resources overall while still achieving our goals, which is a huge practical win for scaling up.

Mira: They are essentially showing that the entanglement of joint measurements is a limiting factor, and their analysis provides the tools to quantify that limit precisely based on how those measurements are imperfect.

Kai: So, in short, they’re providing the math to see exactly how measurement entanglement limits teleportation performance under realistic coherent errors.

Lev: And for us researchers, it gives us a concrete roadmap on what kind of resource trade-offs we should expect when moving from idealized theory to actual laboratory settings.

The paper's summary: Kai: Now that we’ve talked about the setup, let’s summarize what this paper actually boils down to in terms of its core message regarding "Quantum teleportation with partially entangled joint measurements induced by coherent errors." The main point is that standard teleportation assumes perfect Bell-state measurements, but in reality, those measurements are often imperfect due to coherent errors.

Mira: That’s right; the summary emphasizes that these coherent errors deform the ideal Bell basis into a rotated, partially entangled measurement basis parameterized by an error strength 't', which directly causes the success probability of achieving unit-fidelity teleportation to drop.

Lev: I see this as showing that fidelity isn't just about how good our channel is; it’s fundamentally constrained by how well we can perform the joint measurement given the noise in the entangling process.

Kai: Exactly, and they use equations like F tele(t) = two + EM(t) cubed to show that this fidelity decreases as 't' increases, which is a clear quantification of that performance degradation <ref:2605.12130#pg0>.

Mira: Furthermore, their summary highlights the introduction of the measurement-reversal (MR) framework as a proposed strategy to overcome these limits by allowing Bob more flexibility than the standard protocol allows.

Lev: The MR framework lets Bob use an outcome-dependent reversing operation Rr, which is implemented probabilistically to recover the input state, moving beyond just deterministic unitary operations.

Kai: So, it’s a two-pronged approach: first quantifying the degradation using standard metrics, and second offering a generalized protocol that actively fights those limitations through reversal.

Mira: The central theme of the summary is showing that performance is determined by the interplay between channel entanglement and measurement entanglement, with alignment dependence appearing through terms like E c E r x r in Theorem one <ref:2605.12130#pg0>.

Lev: That dependency on both resources and their relative alignment is what makes this analysis so powerful because it shows we can optimize beyond just increasing one resource in isolation.

Kai: It’s a very clear operational interpretation: the maximum success probability is limited by whichever of these two resources—channel entanglement or measurement entanglement—is weaker.

Mira: That’s the key insight for me; it gives us an explicit way to design protocols that balance those competing needs rather than just pushing one resource to its absolute maximum.

Lev: So, we aren't just trying to maximize everything; we have a hard constraint dictated by the weakest link in our system when dealing with these coherent errors.

The paper's improvements: Kai: Moving into the improvements section of "Quantum teleportation with partially entangled joint measurements induced by coherent errors," they detail the specific strategies they suggest to overcome those limitations imposed by partially entangled joint measurements.

Mira: They propose a generalized protocol within the measurement-reversal (MR) framework as their main improvement, allowing for an arbitrary joining of operations at Bob’s side instead of just unitary operations.

Lev: From an error correction viewpoint, this framework is significant because it allows the recovery of the original input state through that outcome-dependent reversing operation Rr which is probabilistic in nature.

Kai: That probabilistic reversal operation Rr means Bob doesn't have to rely on a single deterministic path; he can use classical information from the measurement outcome to choose a specific correction.

Mira: The paper also provides an explicit constraint expressed by the no-cloning constraint, which is d(d + one)L max Alice + (d − one)P max succ 2d, which sets the mathematical boundary for achievable success probability <ref:2605.12130#pg0>.

Lev: That inequality is really important because it gives us a concrete way to assess if a proposed protocol will even be feasible given our hardware's physical limits on Alice’s side and Bob’s side resources.

Kai: The authors also show how this framework can preserve unit teleportation fidelity for pure-state inputs, provided the measurement imperfection is known beforehand.

Mira: That preservation of unit fidelity is conditional on knowing the error model, which means we don't need perfect hardware to achieve perfect results, just good classical post-processing and knowledge of the errors.

Lev: So this moves us away from needing substantial modifications to existing quantum hardware by relying only on classical post-processing and local filtering operations at Bob’s side.

Kai: That’s a very practical takeaway; it suggests we can achieve high fidelity without requiring massive, complex changes to the physical setup itself.

Mira: I think the overall improvement is that they shift the limitation from an unavoidable fidelity loss to a controllable success probability that can be optimized by choosing the right strategy.

Lev: If we are designing systems, this means our focus should be on optimizing that success probability while knowing exactly what fidelity we can expect under those measurement constraints.

Conclusion: Kai: So, wrapping up our discussion on "Quantum teleportation with partially entangled joint measurements induced by coherent errors," the authors conclude that unit-fidelity teleportation can always be restored for pure-state inputs, even when the joint measurement is weakly entangled.

Mira: That’s the final takeaway: we don't need perfect hardware as long as we know the measurement imperfection is known, and they achieve this by leveraging a heralded strategy where imperfections are managed into a controllable success probability.

Lev: I just want to stress that for anyone trying to run this on physical systems, the most important part is understanding how 't' impacts the concurrence EM(t) and then using their bounds to predict performance constraints accurately.

Kai: Exactly, so we have a tool for practical implementation: a framework that lets us achieve high fidelity without needing massive hardware overhauls by relying on classical post-processing.

Mira: The paper really provides a solid foundation showing how measurement entanglement and channel entanglement interact to set the ultimate performance limit in these scenarios.

Lev: I think this work sets a clear benchmark for what resource trade-offs we should be aiming for when designing future quantum systems that incorporate distributed quantum links.

Center for Quantum Technology, Korea Institute of Science and Technology (KIST) · Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University · Division of Quantum Information, KIST School, Korea University of Science and Technology (UST) · School of Computational Sciences, Korea Institute for Advanced Study · Department of Physics, Pohang University of Science and Technology (POSTECH)

quant-ph

Submitted: 2026-05-12

Updated: 2026-10-02

Comments: 14 pages, 11 figures, Revised to match the published version

Journal ref: Phys. Rev. A 114, 042401 (2026)

DOI: 10.1103/py1h-hmn9

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 87/100

The gist: Quantum teleportation performance is fundamentally limited by measurement entanglement in realistic scenarios where joint measurements are imperfect due to coherent errors.

Key concepts

Coherent Error: These are imperfections in the entangling operations used in quantum systems that deform the ideal measurement basis away from a perfect Bell state measurement. This deformation is quantified by an error strength 't' that increases with imperfect entangling time, directly impacting how well the joint measurement is entangled.
Partially Entangled Joint Measurement: When coherent errors occur, the joint measurements performed by Alice and Bob are no longer ideal Bell states but are instead partially entangled. This imperfection limits the maximum success probability of faithful teleportation, as the performance is fundamentally constrained by this weaker entanglement resource.
Measurement-Reversal Framework: This generalized protocol allows Bob to perform a probabilistic reversing operation after his measurement. Unlike standard protocols, which only allow unitary corrections, this framework enables recovery of the original input state through an outcome-dependent reversal, even with imperfect joint measurements.

Terminology

Entanglement — 103× in this paper · explained in 4 episodes
Fidelity — 69× in this paper · explained in 2 episodes
Alignment — 15× in this paper · explained in 1 episode
Information Leakage — 6× in this paper · explained in 2 episodes
Benchmark — 2× in this paper · explained in 2 episodes
Calibration — 1× in this paper · explained in 7 episodes
Core — 1× in this paper · explained in 2 episodes
Effective Hamiltonian — 1× in this paper · explained in 2 episodes
Hybrid Entanglement — 1× in this paper · explained in 2 episodes
Korea Institute of Science and Technology — 1× in this paper
Multipartite Entanglement — 1× in this paper · explained in 2 episodes
Quantum Physics — 1× in this paper · explained in 11 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

Quantum teleportation performance is fundamentally limited by measurement entanglement in realistic scenarios where joint measurements are imperfect due to coherent errors. This work analytically shows how the entanglement of joint measurements determines teleportation performance and proposes a strategy using a measurement reversal framework to recover unit teleportation fidelity despite partially entangled joint measurements.

The Gist

The maximum success probability of faithful teleportation is fundamentally limited by the weaker of the two resources, revealing a clear operational interpretation of measurement entanglement.

Effect of Coherent Error in Quantum Teleportation

In the standard quantum teleportation protocol, performance degrades when joint measurements deviate from an ideal Bell-state measurement (BSM) due to coherent errors. Specifically, coherent errors deform the measurement basis away from the ideal Bell basis, transforming it into a partially entangled one. This deformation is parameterized by an error strength 't', which increases with imperfect entangling time. The resulting average teleportation fidelity in the standard protocol is given by:

(standard): Ftele(t) = 2 + EM(t) cubed, where EM(t) is the concurrence of the deformed Bell basis, decreasing monotonically with t. This demonstrates that coherent errors in BSM can significantly degrade teleportation performance, even when the quantum channel remains perfectly maximally entangled.

Teleportation Protocol in Measurement-Reversal Framework

The paper introduces a generalized protocol within the measurement-reversal (MR) framework to overcome limitations imposed by partially entangled joint measurements. Unlike the standard protocol, which restricts Bob’s correction to unitary operations, the MR framework allows for a more general probabilistic reversing operation at Bob’s side, enabling recovery of the original input state. The post-measurement state at Bob’s side is described by:

(3) ϕ˜r⟩ = (⟨wraa¯ ⊗ Ib)(ϕ⟩a¯ ⊗ Φ⟩ab) = E T W†rϕ⟩b.

This framework allows for the recovery of the input state through an outcome-dependent reversing operation Rr, which is implemented probabilistically. The performance is quantified by the heralded teleportation fidelity and success probability, subject to the no-cloning constraint expressed by:

d(d + 1)L max Alice + (d − 1)P max succ ≤ 2d.

Role of Joint Measurement and Quantum Channel in Faithful Teleportation

The analysis shows that the performance is determined by the interplay between channel entanglement and measurement entanglement. For qubit systems (d=2), Theorem 1 provides an exact characterization:

Theorem 1 states that the maximum success probability for outcome r is given by:

(9) P max succ = 1/4 [(1 + E¯c E¯r xr) - q(1 + E¯c E¯r xr) squared - E 2cE 2r] where x r quantifies the relative alignment between the channel and measurement bases.

This result shows that Ec and Er enter symmetrically through the factor EcEr, and the alignment dependence appears through the term E¯cE¯r xr. The paper concludes that optimizing faithful teleportation requires not only increasing the amount of entanglement in both resources but also choosing their relative basis alignment appropriately.

Applications to Realistic Coherent-Error Models

The framework is applied to realistic coherent error models arising from imperfect entangling operations in quantum systems. For superconducting qubits, a ZZ interaction during entangling evolution is modeled by Uent(t) = exp [-i(π/4)Z a X a + t Z a Z a], where 't' quantifies the error strength. This coherent error continuously reduces the entanglement of the implemented joint measurement, quantified by EM(t) = sin 2R(t), which decreases monotonically with t. The paper demonstrates that while the standard protocol fidelity decreases with t, the optimized protocol within our framework preserves unit teleportation fidelity for known coherent measurement error. This improvement is achieved at the expense of a reduced (heralded) success probability. For a maximally entangled channel, the maximum success probability is given by P max succ = 1 − max[cos 2φ, cos 2R(t)].

Conclusion and Future Directions

The research establishes that unit-fidelity teleportation can always be restored for pure-state inputs, regardless of how weakly entangled the joint measurement is, provided that the measurement imperfection is known. The work provides a practical tool for achieving faithful teleportation without requiring substantial modifications to existing hardware by relying only on classical post-processing and local filtering operations. The findings suggest that "such limitations can be overcome by adopting a heralded strategy, where unit-fidelity teleportation is maintained while imperfections are shifted into a controllable success probability that can be optimized.

Improvements for AI systems

Here are the specific improvements to AI systems that can be made based on this scientific paper, along with what those improved systems could achieve:

) Improvements for AI Systems

The core contribution of this paper is providing a robust framework for quantum teleportation fidelity under realistic, coherent measurement errors by introducing a Measurement-Reversal (MR) protocol. This framework allows for the recovery of unit fidelity even when the joint measurement is imperfect, shifting the performance trade-off from an unavoidable fidelity loss to a controllable success probability.

Here are specific improvements and capabilities derived from this research:

A Novel Quantum State Estimation and Recovery Module (MR-based):
This module replaces standard deterministic quantum teleportation with the Measurement-Reversal (MR) framework, where the receiver performs an optimized probabilistic reversing operation conditioned on the measurement outcome.
It can handle realistic, coherent errors in entangling operations (modeled as ZZ interactions or XX couplings in hardware) without requiring perfect gate fidelity.
The improved AI system can perform heralded teleportation: it can reliably recover the original input quantum state with unit fidelity on every successful measurement outcome, provided the error model is known beforehand.
Entanglement-Aware Resource Optimization Engine:
This engine utilizes the quantitative trade-off relations derived (e.g., Theorem 1 and Theorem 2) connecting channel entanglement, joint measurement entanglement, and success probability.
The AI can dynamically adjust the required resources—specifically, the necessary entanglement of the shared quantum channel versus the required precision/entanglement of Alice's joint measurement—to maximize operational success probability while maintaining unit fidelity (or meeting a target fidelity threshold).
This allows for resource-aware protocol selection, ensuring that computational overhead is only incurred when necessary to maintain high-fidelity results.
Coherent Error Mitigation Strategy:
The system can explicitly model and counteract the effect of coherent errors (like time-dependent rotation parameters, e.g., in the ZZ interaction model) by calculating the optimal reversing operators, such as those derived in Equation (8).
This provides a practical post-processing layer that actively compensates for systematic errors introduced during state preparation or measurement, moving beyond simple stochastic noise correction.
High-Dimensional State Teleportation Architectures:
The framework extends to higher-dimensional systems (d > 2), where the AI can leverage the derived upper and lower bounds (Theorem 2) to predict the performance constraints imposed by measurement entanglement, even when a closed-form solution is unavailable.
This enables the design of teleportation protocols for complex qudit systems, ensuring that performance degradation due to imperfect measurements is strictly bounded and predictable based on the joint measurement's entanglement structure.

) What the Improved AI System Can Do (Specific Applications)

The improved AI system, leveraging these principles, can be applied in several high-stakes quantum computing domains:

Fault-Tolerant Quantum Gate Teleportation:
It can be used to design and execute teleportation protocols for quantum gates within universal quantum computation architectures (e.g., superconducting qubits). The system guarantees that the resulting gate operation will have a fidelity arbitrarily close to unity, even when the physical entangling gates are known to suffer from residual coherent ZZ errors during execution.
Distributed Quantum Network Routing:
For long-distance quantum communication, the AI can optimize entanglement swapping and teleportation links between nodes in a network where intermediate measurement stations (Alice) have imperfect joint measurements. It will select the optimal joint measurement basis configuration that maximizes the successful transmission rate while ensuring that any successful transmission yields a state with unit fidelity, effectively mitigating coherent errors across network segments.
Quantum Sensing and State Transfer:
It can be used to transfer quantum information from a sensor platform (Alice) to a remote processing unit (Bob). By employing the MR framework, the system ensures that if the measurement outcome is successful, the transferred state is perfectly preserved, which is critical for high-precision quantum sensing applications where fidelity directly translates to measurement accuracy.
Hardware Diagnostics and Calibration:
The AI can act as a diagnostic tool by comparing expected performance bounds (derived from its entanglement analysis) against experimental results (measured success probabilities). It can precisely pinpoint whether performance degradation is due to insufficient channel entanglement, poor joint measurement quality, or unmitigated coherent errors, guiding hardware calibration efforts with high precision.

Sources

Teleportation via generalized measurements, and conclusive teleportation