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arxiv: 2512.09856 · v2 · pith:MFSPDTKRnew · submitted 2025-12-10 · 🪐 quant-ph · physics.optics

Practical and Efficient Verification of Entanglement with Incomplete Measurement Settings

Jiheon Seong , Jin-Woo Kim , Seungchan Seo , Seung-Hyun Nam , Anindita Bera , Dariusz Chru\'sci\'nski , June-Koo Kevin Rhee , Heonoh Kim
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Joonwoo Bae
This is my paper

Pith reviewed 2026-05-16 23:08 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords entanglementmeasurementefficientincompleteapproachentangledobservablesonly
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The pith

A small number of measured observables suffices to construct entanglement witnesses that certify quantum states without full tomography.

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

The paper develops a framework that converts estimates from a limited set of observables into many entanglement witnesses for practical verification. This targets the common lab situation where full state tomography requires too many measurement settings to be feasible. A semidefinite program is used to optimize the choice of witness under the given constraints so that entanglement is still detected reliably. The method is shown to work in an experiment with photon-polarization qubits where only a fraction of the usual data was needed. If correct, it lowers the experimental cost of confirming entanglement in resource-limited quantum systems.

Core claim

We show how the experimental estimation of a small number of observables can be directly exploited to construct a large family of entanglement witnesses, enabling the efficient identification of entangled states. An optimization approach formulated as a semidefinite program systematically searches for those witnesses best suited to reveal entanglement under the given measurement constraints, demonstrated in a proof-of-principle experiment with photon-polarization qubits where entanglement is certified using only a fraction of the full measurement data.

What carries the argument

Entanglement witnesses built directly from estimates of a tomographically incomplete set of observables and optimized via semidefinite programming to detect entanglement under measurement limits.

Load-bearing premise

The chosen incomplete observables must still allow construction of witnesses that detect the target entangled states without the optimization introducing false positives.

What would settle it

Preparing a known entangled state, collecting data only on the incomplete observable set, and finding that none of the optimized witnesses yields a negative expectation value would show the framework cannot certify entanglement when it should.

read the original abstract

In this work, we present a practical and efficient framework for verifying entangled states when only a tomographically incomplete measurement setting is available-specifically, when access to observables is severely limited. We show how the experimental estimation of a small number of observables can be directly exploited to construct a large family of entanglement witnesses, enabling the efficient identification of entangled states. Moreover, we introduce an optimization approach, formulated as a semidefinite program, that systematically searches for those witnesses best suited to reveal entanglement under the given measurement constraints. We demonstrate the practicality of the approach in a proof-of-principle experiment with photon-polarization qubits, where entanglement is certified using only a fraction of the full measurement data. These results reveal the maximal usefulness of incomplete measurement settings for entanglement verification in realistic scenarios.

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

2 major / 1 minor

Summary. The paper introduces a framework for constructing entanglement witnesses from a tomographically incomplete set of measured observables. It formulates an SDP optimization to select coefficients that maximize violation on a target state while enforcing positivity constraints on separable states, and demonstrates the method in a proof-of-principle photon-polarization qubit experiment that certifies entanglement using only a fraction of full tomographic data.

Significance. If the witnesses remain valid, the approach would reduce experimental overhead for entanglement verification in resource-constrained settings by exploiting partial measurement data, potentially enabling scalable certification without full state tomography.

major comments (2)
  1. [SDP optimization and witness construction] The SDP positivity constraint is formulated as a relaxation over the span of the measured observables (or a partial-transpose proxy). This does not guarantee non-negativity on separable states whose support lies outside the measured directions, which could produce invalid witnesses and false positives. The construction and experiment sections do not include an explicit check against a dense set of separable states.
  2. [Experimental demonstration] The photon experiment reports successful detection but provides no quantitative error analysis, false-positive rate, or verification that the returned witnesses remain non-negative on separable states outside the incomplete measurement subspace. Without these, the claim that entanglement is certified under the given constraints cannot be fully evaluated.
minor comments (1)
  1. [Abstract] The abstract states that a 'large family' of witnesses is constructed from a small number of observables, but the precise mapping from the incomplete set to the family is not detailed in the provided description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each major comment below, providing clarifications and indicating the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: The SDP positivity constraint is formulated as a relaxation over the span of the measured observables (or a partial-transpose proxy). This does not guarantee non-negativity on separable states whose support lies outside the measured directions, which could produce invalid witnesses and false positives. The construction and experiment sections do not include an explicit check against a dense set of separable states.

    Authors: We appreciate this observation. The SDP is indeed formulated to enforce positivity within the subspace of measured observables using the partial-transpose proxy to ensure the witness is valid for the given constraints. However, to fully address potential concerns about states outside this subspace, we will add in the revised manuscript an explicit numerical check: we will sample a dense set of separable states (e.g., via random mixtures of product states) and verify that the witness expectation value is non-negative for all of them. This verification will be included in the theoretical framework section and applied to the experimental witnesses. revision: yes

  2. Referee: The photon experiment reports successful detection but provides no quantitative error analysis, false-positive rate, or verification that the returned witnesses remain non-negative on separable states outside the incomplete measurement subspace. Without these, the claim that entanglement is certified under the given constraints cannot be fully evaluated.

    Authors: We agree that quantitative error analysis and additional verification would enhance the experimental section. In the revision, we will provide a detailed error propagation analysis for the measured observables and the resulting witness values, including confidence intervals. We will also estimate the false-positive rate by applying the constructed witnesses to simulated noisy separable states consistent with the experimental precision. The non-negativity verification on separable states will be included as part of the above-mentioned checks. These additions will allow for a more complete evaluation of the certification. revision: yes

Circularity Check

0 steps flagged

No circularity; SDP witness optimization is externally grounded

full rationale

The paper constructs entanglement witnesses as linear combinations of a limited set of measured observables and uses a standard semidefinite program to optimize the coefficients while enforcing positivity on separable states. This optimization is an external convex-programming tool applied to the incomplete-measurement data; it does not reduce to a self-definition, a fitted parameter renamed as a prediction, or a self-citation chain. The experimental photon demonstration certifies entanglement on the target state without the validity claim being tautological. No load-bearing uniqueness theorem or ansatz is imported from the authors' prior work in a way that collapses the derivation. The framework remains self-contained against external SDP solvers and standard witness theory.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. The framework relies on standard quantum mechanics and convex optimization.

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Reference graph

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