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arxiv: 2605.26867 · v2 · pith:LHESBKXHnew · submitted 2026-05-26 · 🪐 quant-ph

Entangling power and fidelity diagnostic for bipartite quantum channels

Marcin Rudzi\'nski , Gianluigi Tartaglione , Karol \.Zyczkowski This is my paper

Pith reviewed 2026-06-29 17:10 UTC · model grok-4.3

classification 🪐 quant-ph
keywords bipartite quantum channelsentangling powerconcurrencenegativityfidelityseparable channels2-qubit channelsSchmidt coefficients
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The pith

Fidelity averages over fixed Schmidt orbits in bipartite channels are determined solely by average fidelity and product-input fidelity.

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

The paper shows that for bipartite quantum channels acting on equal-dimensional systems, the average fidelity over any local-unitary orbit of inputs sharing the same Schmidt coefficients depends only on the channel's overall average fidelity and its behavior on product states. It defines new entangling powers for two-qubit channels using concurrence and negativity, proving they are convex, monotone under local operations, and zero exactly for separable channels. These measures are then extended to general inputs with an analytical lower bound provided for the concurrence version.

Core claim

For bipartite channels with equal local dimensions the fidelity averaged over any fixed Schmidt-coefficients local-unitary orbit is completely determined by average input-output fidelity and its restriction to product inputs. Concurrence- and negativity-based entangling powers for 2-qubit channels vanish for all separable channels while being convex and monotone under local postprocessing.

What carries the argument

Concurrence-based and negativity-based entangling power of a quantum channel, obtained by extending the corresponding entanglement measures from states to channels via product inputs.

If this is right

  • The fidelity diagnostic reduces computation to two simpler quantities.
  • Entangling power measures faithfully detect non-separability unlike linear-entropy based ones.
  • Monotonicity under local postprocessing ensures they are valid quantifiers.
  • Generalization allows application to entangled inputs with a lower bound on variation.

Where Pith is reading between the lines

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

  • This fidelity relation may simplify numerical sampling in channel tomography or benchmarking.
  • The new measures could serve as benchmarks for entanglement generation in quantum devices.
  • Extending to higher dimensions might require similar orbit arguments.

Load-bearing premise

That concurrence and negativity extend to channel entangling power such that the resulting quantities vanish precisely on separable channels.

What would settle it

A separable channel for which the concurrence-based entangling power is nonzero, or an explicit counterexample where orbit-averaged fidelity is not fixed by the two quantities.

Figures

Figures reproduced from arXiv: 2605.26867 by Gianluigi Tartaglione, Karol \.Zyczkowski, Marcin Rudzi\'nski.

Figure 2
Figure 2. Figure 2: FIG. 2: False-positive behavior of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: False-positive behavior of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Controlled-phase unitary benchmark. Since the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: summarizes the fidelity-bias parameter for all discussed models. V. BOUNDS FOR CONCURRENCE-BASED ENTANGLING POWER The concurrence-based entangling power eC (Φ) is a genuine entanglement-generation diagnostic, but it is gen￾erally difficult to evaluate analytically. The difficulty comes from the nonlinear dependence of concurrence on the output state. In this section we derive computable analytic bounds on … view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Comparison between the concurrence-based entangling power [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Average concurrence variation for the correlated phase-damping channel, Eqs. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Average concurrence variation for the controlled-phase evolution under correlated phase damping –see [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

We study two complementary diagnostics of bipartite quantum channels, namely fidelity preservation across different classes of input states and entanglement generation from product inputs, given by properly defined entangling power for bipartite channels. We show that the fidelity averaged over any fixed Schmidt-coefficients local-unitary orbit for equal local dimensions is completely determined by average input-output fidelity and its restriction to product inputs. We also introduce concurrence- and negativity-based entangling power for 2-qubit channels, prove their convexity and monotonicity under local postprocessing, and show that, unlike the previously proposed linear-entropy quantity, they vanish for all separable channels. Examples of non-separable channels are investigated. Finally, we generalize our definitions of entangling power to non-product inputs, and provide an analytical lower bound for the concurrence-based entanglement variation, showing its effectiveness with specific examples.

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.

Referee Report

0 major / 3 minor

Summary. The manuscript introduces fidelity-based diagnostics for bipartite quantum channels and defines concurrence- and negativity-based entangling powers for 2-qubit channels. It claims that, for equal local dimensions, the average fidelity over any fixed Schmidt-coefficient local-unitary orbit is completely determined by the average input-output fidelity and its restriction to product inputs. The new entangling powers are shown to be convex and monotone under local postprocessing, and to vanish exactly on separable channels (unlike the linear-entropy version). The definitions are extended to non-product inputs, and an analytical lower bound is given for the concurrence-based entanglement variation, illustrated with examples.

Significance. If the stated proofs hold, the work supplies improved, separability-detecting measures of channel entangling power together with a useful reduction for orbit-averaged fidelity. These are concrete advances over existing linear-entropy diagnostics and could be adopted for channel characterization in quantum information.

minor comments (3)
  1. The explicit definitions of the concurrence- and negativity-based entangling powers (product-input versions) should be displayed as numbered equations in the main text rather than only in the abstract or introduction, to facilitate direct verification of the vanishing property on separable channels.
  2. Notation for the local-unitary orbit averaging (e.g., the measure on the orbit and the fixed Schmidt coefficients) is introduced without a dedicated preliminary subsection; a short paragraph or equation block clarifying the averaging procedure would improve readability.
  3. The generalization to non-product inputs and the analytical lower bound for concurrence-based variation are presented late; moving the lower-bound statement to the section on the product-input case would better highlight its relation to the main results.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, including the summary of our results on fidelity diagnostics and concurrence-/negativity-based entangling powers, as well as the significance evaluation. We note the recommendation for minor revision; however, the report contains no specific major comments requiring point-by-point responses.

Circularity Check

0 steps flagged

No significant circularity; derivations rest on explicit definitions and standard properties

full rationale

The paper introduces concurrence- and negativity-based entangling powers via direct definitions from product inputs and standard state measures, then proves convexity, monotonicity, and vanishing on separable channels using those definitions. The fidelity-orbit identity is presented as a direct averaging consequence for equal dimensions. No load-bearing step reduces to a self-citation chain, fitted parameter renamed as prediction, or self-definitional loop. The mention of a prior linear-entropy quantity is non-central and does not affect the new claims. The derivation chain is self-contained against external benchmarks of entanglement theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

Abstract-only review supplies no explicit free parameters or invented entities beyond the new definitions themselves; standard quantum-channel axioms are presupposed.

axioms (1)
  • domain assumption Concurrence and negativity are valid entanglement monotones that can be lifted to channel-level functionals
    Invoked when defining the new entangling powers and proving they vanish on separable channels.
invented entities (2)
  • Concurrence-based entangling power for channels no independent evidence
    purpose: Quantify entanglement generation from product inputs
    New functional introduced in the paper; no independent evidence supplied in abstract.
  • Negativity-based entangling power for channels no independent evidence
    purpose: Quantify entanglement generation from product inputs
    New functional introduced in the paper; no independent evidence supplied in abstract.

pith-pipeline@v0.9.1-grok · 5676 in / 1202 out tokens · 36549 ms · 2026-06-29T17:10:21.941822+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Characterizing quantum channels from local-unitary invariants

    quant-ph 2026-06 unverdicted novelty 6.0

    Develops moments from local-unitary invariants via Haar integrals to characterize entanglement behavior of two-qubit channels, with second-order moments yielding criteria for non-entangling and entanglement-breaking channels.

Reference graph

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    Choose an orthonormal basis{|µ⟩}D µ=1ofH A⊗HB, and write Kµν:=⟨µ|K|ν⟩

    Average input–output fidelity.For a fixed Kraus operatorK, define f(K) := ∫ dψ ⏐⏐⟨ψ|K|ψ⟩ ⏐⏐2 , F(Φ) = ∑ α f(Kα). Choose an orthonormal basis{|µ⟩}D µ=1ofH A⊗HB, and write Kµν:=⟨µ|K|ν⟩. A Haar-random pure state onCD can be written as |ψ⟩=W|0⟩, W∈U(D), with|0⟩a fixed basis vector. Then f(K) = ∫ dW ⏐⏐⟨0|W†KW|0⟩ ⏐⏐2 = D∑ µ,ν,κ,λ=1 KµνK∗ κλ ∫ dW W∗ µ0Wν0Wκ0W∗ λ...

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