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arxiv: 2405.08065 · v1 · submitted 2024-05-13 · 🪐 quant-ph

Direct and Efficient Detection of Quantum Superposition

Daniel Kun , Teodor Str\"omberg , Michele Spagnolo , Borivoje Daki\'c , Lee A. Rozema , Philip Walther This is my paper

Pith reviewed 2026-05-24 00:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum superpositionXOR gamelocal measurementsverification schemesingle photonresource efficiencyquantum witness
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The pith

An adapted XOR game verifies quantum superposition using only local measurements and a second independent particle.

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

The paper adapts a classical XOR game so that separated parties measure complementary parts of a particle and use the outcomes, together with measurements on an independent helper particle, to certify that the first particle occupies a superposition. This approach avoids the need to recombine the superposed components, which most existing verification methods require. The game is converted into a verification protocol in which the probability of correctly identifying superposition grows exponentially with the number of copies tested. An experiment with single photons reaches 99 percent that the particle is superposed after testing only 37 copies.

Core claim

Mapping the certification of superposition onto an XOR game in which one party measures one basis and the other measures a complementary basis, then correlating results with an independent auxiliary particle, produces a witness whose success probability exceeds the classical bound and approaches unity exponentially fast in the number of trials, all while using strictly local operations.

What carries the argument

The adapted XOR game, which turns local measurement outcomes on split parts of the superposed particle plus an independent helper into a statistical witness that the input state is superposed.

If this is right

  • Superposition can be verified without any recombination or interference of the distinct states.
  • Statistical confidence grows exponentially while the number of copies needed grows only linearly.
  • The method operates with single photons and requires only local measurements.
  • XOR games can serve as witnesses for quantum resources other than entanglement.

Where Pith is reading between the lines

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

  • The protocol could be used in distributed settings where physical recombination of paths is impossible.
  • Similar game constructions might certify coherence or other superposition-like features in more complex systems.
  • The exponential scaling suggests the approach could become practical for routine resource certification in quantum networks.

Load-bearing premise

The helper particle must be fully independent, with no hidden correlations or measurement imperfections that could produce the same game statistics without the target particle actually being in superposition.

What would settle it

The winning probability of the adapted game remains at or below the classical bound when the input particle is prepared in a known superposition state.

Figures

Figures reproduced from arXiv: 2405.08065 by Borivoje Daki\'c, Daniel Kun, Lee A. Rozema, Michele Spagnolo, Philip Walther, Teodor Str\"omberg.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: ). Moreover, as shown in the inset of the figure, the confidence approaches unity exponentially fast with the number of copies. Discussion.— In this work we have demonstrated the superposition principle for a quantum particle using spa￾tially separated local measurements only. To do so we created a nonlocal interferometer, wherein the individual phases of a superposed photon are measured nonlocally, withou… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Simplified schematic of setup with labeled modes [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Piezo voltage sweep defining the set points for phases ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Relative detection efficiency is determined by performing pairwise linear regression of coincidence patterns, collected [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. HOM visibility measurement on Alice’s detection setup. Data points are collected with a 5 s integration time and are [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

One of the most striking quantum phenomena is superposition, where one particle simultaneously inhabits different states. Most methods to verify coherent superposition are indirect, in that they require the distinct states to be recombined. Here, we adapt an XOR game, in which separated parties measure different parts of a superposed particle, and use it to verify superpositions with \textit{local measurements} and a second independent particle. We then turn this game into a resource-efficient verification scheme, obtaining a confidence that the particle is superposed which approaches unity exponentially fast. We demonstrate our scheme using a single photon, obtaining a 99\% confidence that the particle is superposed with only 37 copies. Our work shows the utility of XOR games to verify quantum resources, allowing us to efficiently detect quantum superposition without reinterfering the superposed states.

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 claims to adapt an XOR game, in which separated parties measure different parts of a superposed particle, into a verification scheme that uses only local measurements plus a second independent particle to certify superposition. The scheme is presented as resource-efficient, with the confidence that the particle is superposed approaching unity exponentially fast in the number of copies. An experimental demonstration with a single photon is reported to achieve 99% confidence using only 37 copies.

Significance. If the central claim holds with the required controls, the work would provide a direct method for certifying superposition without state recombination, which is useful in settings where interference is impractical. The game-theoretic framing for quantum resource verification and the reported exponential scaling in copies are potentially valuable contributions if the classical/quantum bounds and experimental assumptions are rigorously established.

major comments (2)
  1. [Abstract] Abstract: the reported 99% confidence with 37 copies provides no details on error bars, post-selection criteria, or controls for the local-measurement assumption and second-particle independence; these are load-bearing for the certification claim and the exponential confidence bound.
  2. [Scheme description / game adaptation] The adaptation of the XOR game requires explicit classical and quantum winning probabilities (or bounds) under strictly local measurements and an independent auxiliary particle; without these derivations or tables, it is unclear whether observed statistics certify superposition exclusively or could be mimicked by classical correlations or imperfections.
minor comments (1)
  1. [Abstract / Title] The title uses 'Direct' but the scheme relies on an auxiliary particle and game statistics; a brief clarification of this terminology would improve precision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We provide point-by-point responses to the major comments below. We agree that additional details are needed to strengthen the presentation and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reported 99% confidence with 37 copies provides no details on error bars, post-selection criteria, or controls for the local-measurement assumption and second-particle independence; these are load-bearing for the certification claim and the exponential confidence bound.

    Authors: The abstract summarizes the key result but omits experimental specifics for brevity. We will revise the abstract to briefly note the statistical confidence interval, lack of post-selection, and verification of local measurements and particle independence. These details are elaborated in the experimental section, but we concur that the abstract should highlight them to support the claim. revision: yes

  2. Referee: [Scheme description / game adaptation] The adaptation of the XOR game requires explicit classical and quantum winning probabilities (or bounds) under strictly local measurements and an independent auxiliary particle; without these derivations or tables, it is unclear whether observed statistics certify superposition exclusively or could be mimicked by classical correlations or imperfections.

    Authors: In the theoretical development, we calculate the winning probabilities for the adapted XOR game. To make this explicit as requested, we will add a table listing the classical and quantum bounds under strictly local measurements with the independent auxiliary particle. This will show that the certification relies on exceeding the classical limit. revision: yes

Circularity Check

0 steps flagged

No circularity: XOR-game adaptation for superposition verification is self-contained

full rationale

The paper adapts a standard XOR game from quantum information theory to certify superposition via local measurements on separated parts plus an independent second particle, then converts the game into an exponential-confidence verification protocol. No equations, derivations, or self-citations in the abstract or described scheme reduce the claimed winning probability or confidence bound to a fitted parameter defined by the same data, a self-definition, or a load-bearing self-citation chain. The central result remains independent of the target claim and is grounded in externally verifiable game-theoretic bounds.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, invented entities, or non-standard axioms; the scheme implicitly assumes standard quantum mechanics and the validity of the XOR-game mapping to superposition certification.

axioms (1)
  • domain assumption An XOR game can be adapted to certify quantum superposition via local measurements on separated parts plus an independent auxiliary particle.
    Central to the verification scheme described in the abstract.

pith-pipeline@v0.9.0 · 5684 in / 1211 out tokens · 20917 ms · 2026-05-24T00:52:12.754346+00:00 · methodology

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