Measurements on the separated subsystems of an entangled state

Gregory D. Scholes

REVIEW

Measurements on the separated subsystems of an entangled state

Gregory D. Scholes

Quantum Physics · Submitted 3 Sep 2026

Pith's verdict: An intriguing abstract with a clear central claim, but the claim is asserted rather than demonstrated and the math cannot be assessed without the full text—worth referee time only if the derivation actually exists.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on September 9, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

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arXiv ID2609.04178 (version 3)

Pith IDJY2JNRJP, Pith's permanent record of this paper and its review

CitationGregory D. Scholes. "Measurements on the separated subsystems of an entangled state." arXiv:2609.04178 (2026). https://pith.science/paper/JY2JNRJP

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

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Editor's note

read the letter

What you should know: this is an abstract-only submission, and the abstract makes one strong constructive claim: the projections for separated-subsystem measurements on any entangled state come from cosets in the free vector space from which the tensor product space is built. If the full paper actually proves that and shows the probabilities match the Born rule, this is a major foundations result—it would replace collapse with a deterministic local-projection picture. Nothing in the abstract lets us verify that.

What the paper does well: it names a real problem. Given a bipartite state in tensor-product form, it is not generally obvious which local states are detected by measuring A and B, except for separable states. The free-vector-space coset approach is a nontrivial idea and, as far as I can tell from the abstract, not a repackaging of the standard partial-trace machinery. The writing is clear about what it is trying to do. That counts for something.

Soft spots: the central assertion is exactly where the available text is thinnest. We are told the result, not shown it. There is no definition of the cosets, no mapping from cosets to projection operators, no derivation of the measurement probabilities, and no worked example—not even a Bell pair. Without that, eliminating random collapse and explaining nonlocality as local projections is interpretive wrapping around an unverified construction. The stress-test note is fair as far as it goes. The caveat is that absence from the abstract is not absence from the full paper; if the full text supplies the derivation, the concern evaporates. I would want to see how the construction handles a Bell pair and whether it reproduces standard correlations before taking the conceptual claims seriously.

One more thing: the abstract contains no references, so I cannot judge novelty against prior work on local subsystem decompositions, reduced density matrices, or earlier attempts to derive collapse without a collapse postulate. If the full paper does not engage that literature, that is a problem; if it does, fine.

Bottom line: the paper's importance depends entirely on the proof and examples, which we do not have. I would not desk-reject it out of hand, and I would not accept it based on the abstract. Get the full manuscript, check the math, and if the derivation is actually there, send it to a serious referee.

Referee report

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The paper

The paper claims

Measurements on separated entangled subsystems can be fully described by local projections using a coset construction, eliminating collapse and reinterpreting nonlocality as local.

The reading

The paper seeks to show that when we measure the physically separated parts of an entangled composite system, the outcomes are governed purely by projections within each subsystem's local Hilbert space. The author identifies these projections with cosets of states in the free vector space from which the tensor product space is built. If correct, this would remove the random collapse of the wavefunction from the measurement story and recast nonlocality as a natural outcome of how each side projects its possible measurement results. A sympathetic reader would care because the result offers a purely local, collapse-free account of entanglement, potentially clarifying the foundations of quantum measurement.

What carries the argument

The key object is the construction of cosets of states in the free vector space from which the tensor product space of composite quantum systems is defined. These cosets are claimed to represent the effective states of separated subsystems that yield the measurement projections detected locally.

Extended reading notes

Core claim

The central claim is that for any general entangled state, the projections detected by measurements on separated subsystems correspond to (cosets of) states in the free vector space that underlies the tensor product space. By working with these cosets, one obtains the relevant local states without invoking random collapse, so nonlocality emerges from the way each subsystem's measurement projects the set of possible outcomes.

Load-bearing premise

The paper assumes that measurements on a physically separated subsystem are correctly represented by projections in that subsystem's local Hilbert space, and that the coset construction from the free vector space reproduces the same empirical content as the standard tensor-product measurement calculus for any entangled state.

Editorial extensions

If this is right

The standard collapse postulate can be discarded from the description of measurements on entangled states, simplifying the ontology of quantum mechanics.
Nonlocality of entanglement becomes a derived effect from local projection of measurement outcomes rather than an irreducible nonlocal influence.
The measurement calculus for separated subsystems reduces to a local procedure, potentially allowing experimental predictions to be calculated without referencing the global wavefunction.
The coset construction may extend to multipartite entanglement and provide a unified framework for all local measurements on composite systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the coset projections reproduce all standard Born-rule probabilities, this could challenge interpretations that rely on wavefunction collapse as a physical process, possibly favoring a no-collapse or relational view.
The free-vector-space approach might yield new constraints on hidden-variable models by clarifying which local measurement statistics are genuinely accessible without global information.
One could test the construction by deriving explicit coset states for a two-qubit singlet and verifying that marginal statistics match the standard predictions, then extending to more complex entangled states.

Original abstract

The entangled states of composite quantum systems are well studied. The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems. Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space of each subsystem, but to date it has not been clear how to elucidate the relevant states of the separated subsystems because it is not obvious how to resolve them from states given in the tensor product basis, except for the separable states. Here it is shown that the projections of any general entangled state that are detected by measurements on the separated subsystems can be obtained considering the corresponding (cosets of) states in the free vector space from which the tensor product space is defined. The result eliminates the need to invoke random collapse, and from this perspective nonlocality arises because of the way measurements on each separated subsystem projects possible measurement outcomes.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,384 input tokens.

What the abstract itself states, as probabilities: claims first 0.18 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.03 · states quantitative result 0.03 · compares with prior results 0.51 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The entangled states of composite quantum systems are well studied. The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems. Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space of each subsystem, but to date it has not been clear how to elucidate the relevant states of the separated subsystems because it is not obvious how to resolve them from states given in the tensor product basis, except for the separable states. Here it is shown that the projections of any general entangled state that are detected by measurements on the separated subsystems can be obtained considering the corresponding (cosets of) states in the free vector space from which the tensor product space is defined. The result eliminates the need to invoke random collapse, and from this perspective nonlocality arises because of the way measurements on each separated subsystem projects possible measurement outcomes.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The entangled states of composite quantum systems are well studied.	background 1.00	0.03	0.01	asserted 1.00
s1	The particle-like nature of these systems also means that, while entangled, they can be physically separated and measurements performed on the separated subsystems.	background 1.00	0.05	0.03	asserted 0.93
s2	Measurements on the separated subsystems A and B should pertain to vectors in the local Hilbert space of each subsystem, but to date it has not been clear how to elucidate the relevant states of the separated subsystems because it is not obvious how to resolve them from states given in the tensor product basis, except for the separable states.	gap 1.00	0.05	0.04	asserted 0.91
s3	Here it is shown that the projections of any general entangled state that are detected by measurements on the separated subsystems can be obtained considering the corresponding (cosets of) states in the free vector space from which the tensor product space is defined.	contribution 0.65	0.93	0.84	asserted 1.00
s4	The result eliminates the need to invoke random collapse, and from this perspective nonlocality arises because of the way measurements on each separated subsystem projects possible measurement outcomes.	interpretation 0.99	0.78	0.56	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Discussion

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