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arxiv: 2606.03699 · v1 · pith:7M5O5RE4new · submitted 2026-06-02 · 🪐 quant-ph

Certifying coherence in quantum devices under classical control

Gabriele Cobucci , Nicola D'Alessandro , Raphael Brinster , Alexander Bernal , Nikolai Wyderka , Armin Tavakoli This is my paper

Pith reviewed 2026-06-28 09:56 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum coherencesemidefinite programminghidden classical controlcoherence certificationjoint measurabilityquantum channelsquantum superposition
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The pith

A hierarchy of semidefinite programs fully characterises coherence in quantum devices even when hidden classical parameters affect the preparation.

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

The paper establishes methods to certify quantum coherence when preparation devices can be influenced by classical parameters inaccessible to the experimenter. It proves that coherence admits a complete characterisation via a hierarchy of semidefinite programs. Practical versions of the programs remain efficient for devices that output many states, including high-dimensional ones. For qubits the approach connects to joint measurability and scales beyond one thousand states. The same tools also test whether quantum channels preserve coherence or break it.

Core claim

We prove that coherence can be fully characterised through a hierarchy of semidefinite programs. We introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for preparation devices generating many, potentially high-dimensional, quantum states. For the important special case of qubits, we further exploit conceptual connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubits. Finally, we apply these methods to determine whether quantum channels are able to preserve coherence or are inherently coherence-breaking.

What carries the argument

Hierarchy of semidefinite programs that characterises coherence under the model of hidden classical control on the preparation device.

If this is right

  • Coherence certification becomes possible in experiments where the preparation device is subject to inaccessible classical parameters.
  • Computationally tractable programs suffice for accurate certification when many states are generated.
  • For qubit systems the method scales to more than one thousand states while retaining high accuracy.
  • Quantum channels can be classified as coherence-preserving or coherence-breaking using the same programs.

Where Pith is reading between the lines

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

  • The same hierarchy structure could be examined for certifying other quantum resources such as entanglement when similar control limitations apply.
  • Protocol designers might incorporate these certification tests to verify superposition under realistic device constraints.
  • Numerical checks on small known coherent states could confirm convergence of the hierarchy in practice.

Load-bearing premise

The model of hidden classical control correctly describes the experimental scenario in which the experimenter lacks access to some classical parameters that affect state preparation.

What would settle it

A concrete set of quantum states prepared under a known hidden classical control for which the SDP hierarchy returns a value strictly different from the true coherence measure computed by other means would falsify the claim of full characterisation.

Figures

Figures reproduced from arXiv: 2606.03699 by Alexander Bernal, Armin Tavakoli, Gabriele Cobucci, Nicola D'Alessandro, Nikolai Wyderka, Raphael Brinster.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Quantum states that do not commute exhibit coherence, but only when the device preparing them is assumed to be unaffected by classical parameters inaccessible to the experimenter. Such hidden classical control arises both in fundamental tests of quantum phenomena and in quantum information protocols that operate under limited control assumptions. Here, we address the problem of coherence certification by developing complete and practically efficient methods. First, we prove that coherence can be fully characterised through a hierarchy of semidefinite programs. Second, we introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for preparation devices generating many, potentially high-dimensional, quantum states. For the important special case of qubits, we further exploit conceptual connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubits. Finally, we apply these methods to determine whether quantum channels are able to preserve coherence or are inherently coherence-breaking. Together, these results provide a powerful toolbox for analysing quantum superposition in the presence of hidden classical control.

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 paper claims to fully characterize quantum coherence in preparation devices subject to hidden classical control (inaccessible classical parameters) via a complete hierarchy of semidefinite programs, supplemented by a practical SDP method for efficiency with many/high-dimensional states, an exact joint-measurability method for qubits that scales beyond 1000 qubits, and an application determining whether quantum channels preserve or break coherence.

Significance. If the central claims hold, the work supplies a complete, computationally tractable toolbox for coherence certification under realistic limited-control assumptions relevant to both foundational tests and quantum information protocols. The SDP hierarchy provides a parameter-free complete characterization, the qubit reduction offers an exact scalable alternative, and the channel application extends the framework; these are concrete strengths for the field.

minor comments (3)
  1. The abstract states that the practical SDP 'achieves useful accuracy' but does not quantify the accuracy metric or the number/dimensions of states used in the reported examples; adding a brief numerical summary would improve clarity without altering the central claims.
  2. Section introducing the hidden-classical-control model would benefit from an explicit early definition of the inaccessible parameter set (e.g., a short paragraph or equation) to aid readers unfamiliar with the modeling choice.
  3. In the qubit joint-measurability reduction, the scaling claim to 'more than one thousand qubits' should be accompanied by a brief statement of the computational resources or time required for the largest case to substantiate practicality.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of our contributions, and recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central claim is a mathematical proof that coherence under hidden classical control is fully characterized by an SDP hierarchy, derived from standard semidefinite programming and joint-measurability theory. No equations or steps in the provided abstract reduce any prediction or result to a fitted parameter, self-definition, or self-citation chain; the modeling assumptions are explicitly declared upfront rather than smuggled in. The qubit reduction and channel analysis are presented as derived methods, not renamings or ansatzes justified only by prior author work. The derivation chain is self-contained against external benchmarks of SDP completeness and joint measurability, with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities are stated. Standard quantum information assumptions (e.g., validity of SDP relaxations for quantum properties) are implicit but not detailed.

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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. Semidefinite-programming hierarchies for classically simulable state families

    quant-ph 2026-06 unverdicted novelty 7.0

    A complete SDP hierarchy is constructed for classically simulable state families by reformulating the problem as feasibility over deterministic response functions and rank-one projective POVMs.

Reference graph

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