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arxiv: 2606.05884 · v1 · pith:AAZHOAR2new · submitted 2026-06-04 · 🪐 quant-ph

No-go theorems on simulating uncertainty principle's signatures

Chung-Yun Hsieh , Minjeong Song , Shin-Liang Chen This is my paper

Pith reviewed 2026-06-28 01:09 UTC · model grok-4.3

classification 🪐 quant-ph
keywords uncertainty principlecomplementary instrumentsno-go theoremssingle measurement simulationquantum informationclassical information transmissionquantum pre- and post-processing
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The pith

Strong signatures of the uncertainty principle cannot be simulated by any single measurement, even with quantum pre- or post-processing.

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

The paper establishes a series of noise-robust no-go theorems showing that sufficiently strong features tied to the uncertainty principle resist simulation by one measurement, no matter what quantum operations occur before or after it. These features are captured by complementary instruments. The authors give a complete, numerically computable characterization of such instruments and prove they are exactly the resources needed to gain an advantage in a concrete task of sending classical information without ambiguity. A sympathetic reader would conclude that advantages previously attributed to the uncertainty principle cannot be reduced to single-measurement procedures.

Core claim

Strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information.

What carries the argument

Complementary instruments, which model the non-simulable signatures of the uncertainty principle and act as the exact resources required for operational advantage in unambiguous classical information transmission.

If this is right

  • Complementary instruments are required for any advantage in the unambiguous classical information task that single measurements cannot match.
  • The numerical measure provides a practical test for whether given instruments exhibit the non-simulable complementarity.
  • The no-go results remain valid in the presence of noise, limiting what pre- and post-processing can achieve.
  • Quantum advantages previously linked to uncertainty must rely on resources beyond any single measurement.

Where Pith is reading between the lines

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

  • Experimental protocols aiming to exploit uncertainty-principle advantages should check for the presence of complementary instruments rather than uncertainty alone.
  • The results suggest that other quantum features claimed to yield advantages may also require resources that resist single-measurement simulation.
  • If the characterization holds, one could design information tasks whose performance directly quantifies the degree of complementarity present.

Load-bearing premise

Modeling the uncertainty principle's non-simulable features by complementary instruments accurately identifies what single measurements cannot reproduce.

What would settle it

An explicit construction of a single measurement (with or without quantum pre- or post-processing) that achieves the same unambiguous classical information transmission advantage as a pair of complementary instruments would refute the no-go theorems.

Figures

Figures reproduced from arXiv: 2606.05884 by Chung-Yun Hsieh, Minjeong Song, Shin-Liang Chen.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
read the original abstract

Uncertainty principle, one of the most iconic features of quantum mechanics, was originally viewed as a fundamental limitation. Since the inception of quantum information science, researchers began to use it to achieve quantum advantages. To better understand the origin of these advantages, an essential question is: To what extent can the uncertainty principle's signatures be simulated by a single measurement? As a single measurement clearly cannot demonstrate the uncertainty principle, such a simulation, if exists, implies the claimed advantages may either stem from other quantum features, or just be reproducible in a less resourceful way. In this work, we report a series of noise-robust no-go theorems, showing that strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information.

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 / 2 minor

Summary. The paper establishes noise-robust no-go theorems showing that sufficiently strong signatures of the uncertainty principle—modeled via complementary instruments—cannot be simulated by any single measurement, even when assisted by quantum pre- or post-processing. It supplies a complete, numerically feasible characterization of complementary instruments and proves that these instruments are necessary and sufficient resources for an operational advantage in an unambiguous classical-information transmission task.

Significance. If the central claims hold, the work supplies a rigorous, operationally grounded separation between uncertainty-principle signatures and those reproducible by single measurements. The computable measure for complementarity and the necessity-sufficiency result for the communication task furnish concrete tools for distinguishing quantum resources, with direct relevance to quantum communication and measurement theory. The explicit noise-robustness strengthens applicability beyond idealised settings.

minor comments (2)
  1. [Abstract] The abstract states that complementary instruments are 'completely characterised by a numerically feasible measure,' yet the precise definition of this measure and the proof of its completeness are not referenced to a specific theorem or section in the provided abstract; a pointer to the relevant result (e.g., Theorem X in §4) would improve readability.
  2. [Abstract] The operational task is described as 'unambiguously send classical information,' but the precise figure of merit (success probability, error exponent, etc.) and how the advantage is quantified are not stated in the abstract; adding one sentence clarifying the task's payoff function would aid readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper models uncertainty signatures via complementary instruments, provides a computable characterization of them, and proves they are necessary and sufficient for an operational advantage in unambiguous classical information transmission. This establishes noise-robust no-go results against single-measurement simulation (with pre/post-processing). The chain is self-contained: the modeling choice is tied directly to the operational task rather than asserted circularly, the characterization is derived from quantum instrument theory, and the necessity/sufficiency follows from standard quantum mechanics without reducing to fitted inputs, self-definitional loops, or load-bearing self-citations. No equations or steps in the provided structure collapse by construction to their own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, invented entities, or ad-hoc axioms are stated. Relies on standard quantum mechanics and operational task definitions.

axioms (1)
  • standard math Standard postulates of quantum mechanics and the operational framework for instruments and measurements
    The work is situated in quantum information theory and uses the language of instruments without introducing new axioms.

pith-pipeline@v0.9.1-grok · 5697 in / 1164 out tokens · 23210 ms · 2026-06-28T01:09:17.045894+00:00 · methodology

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Reference graph

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