Quantum Monogamy with Predetermined Events

The concept of correlation appears straightforward: measurement outcomes coincide, and patterns emerge. For any record of events, the coefficients are uniquely determined. Thus, if correlations change spontaneously, as seen in quantum monogamy, then individual behavior must have changed first. Surprisingly, this is not always true. When two observables are mutually exclusive, they cannot coincide objectively and need to be grouped across time. Yet, sectioning the flow of events into “iterations” is not trivial in this case. Even with blind windows of coincidence, the same order of outcomes can produce different coefficients of correlation, depending on the number of joint measurements. Therefore, quantum monogamy can happen with fixed pre-determined events. A new concept (“subjective correlation”) is required to explain this phenomenon.

💡 Research Summary

The paper “Quantum Monogamy with Predetermined Events” puts forward a classical, deterministic toy model that allegedly reproduces the hallmark feature of quantum monogamy – the fact that the strength of correlations between two parties changes when a third party is added – without invoking any non‑local or indeterministic physics. The author constructs a “wheel‑of‑fortune” device consisting of eight sectors arranged in a closed cycle. Four binary variables (A₁, B₁, A₂, B₂) are placed on the wheel in a fixed order, with the four positive values occupying one half of the wheel and the four negative values the other half. As the wheel spins, only the sector under a fixed arrow is “actualized” at any instant; this event is recorded together with a timestamp. Because the four observables are mutually exclusive (they never exist simultaneously), any joint measurement must be created artificially by grouping events that occur at different times within a chosen coincidence window.

Two distinct coincidence windows are examined. The first, a “quadruple window,” is wide enough to capture four successive events (one full cycle of the wheel). In this case the four possible pairings (A₁‑B₁, B₁‑A₂, A₂‑B₂, B₂‑A₁) always consist of either (+,+) or (‑,‑). Consequently each expectation value E equals +1, and the CHSH combination S = E(A₁,B₁)+E(B₁,A₂)+E(A₂,B₂)‑E(B₂,A₁) evaluates to the classical bound S = 2. No Bell violation occurs.

The second window, a “pairwise window,” is narrow enough to include only two successive events. Here the pairing of A₁ with B₂ now straddles the boundary between the positive and negative halves of the wheel, so the only possible outcomes are (+,‑) or (‑,+), giving E(A₁,B₂)=‑1. The other three pairings remain (+,+) or (‑,‑) and retain E=+1. Substituting these values into the CHSH expression yields S = 4 (or, after normalisation, the maximal quantum value 2√2), i.e. a maximal Bell violation. Thus the same underlying deterministic record of events can produce either a classical or a quantum‑like correlation pattern solely by changing how the experimenter groups the data.

The author labels this dependence on the observer’s choice of grouping “subjective correlation” and argues that quantum monogamy does not require any exotic resources such as non‑local hidden variables, super‑determinism, or retro‑causality. Instead, the phenomenon is presented as a purely combinatorial effect that arises whenever mutually exclusive observables are forced into joint measurements. The paper further claims that this insight undermines the need for “new physics” to explain quantum correlations and even suggests that quantum cryptography could be improved by exploiting the “subjective” nature of the correlations.

While the construction is mathematically consistent, several critical issues arise. First, the model assumes a fixed, pre‑programmed sequence of measurement outcomes, violating the freedom‑of‑choice assumption that underlies Bell tests; in real experiments the measurement settings are chosen randomly and independently of any hidden variables. Second, the ability to switch coincidence windows after data collection is equivalent to post‑selection, a practice explicitly forbidden in loophole‑free Bell experiments because it can artificially inflate correlations. Third, the model ignores practical experimental constraints such as detector inefficiencies, timing jitter, and the necessity of space‑like separation, all of which are essential to rule out local realistic explanations. Consequently, the “subjective correlation” demonstrated here is better understood as a statistical artefact rather than a genuine reproduction of quantum monogamy.

In summary, the paper offers an intriguing classical illustration that the same deterministic data set can yield different CHSH values depending on how events are grouped, thereby mimicking the apparent monogamy of quantum entanglement. However, because the construction relies on post‑selection‑like grouping, predetermined measurement settings, and the neglect of key Bell‑test assumptions, it does not provide a viable alternative to the standard non‑local interpretation of quantum correlations. The work is valuable as a pedagogical example of how data analysis choices can affect observed correlations, but it falls short of overturning the established understanding of quantum monogamy.