## 1. Introduction

## 2. Background Considerations

_{Q}). Quantum entanglement is verified when the following inequality is violated:

_{k}}, {Λ

_{l}}, {Λ

_{m}}, {Λ

_{n}} represent the four different partitionings of Λ corresponding to the four different pairs of vectors” [24]. The full details of this demonstration can be found in the cited paper, but the relevant conclusion, for the purpose of this investigation, is that the four sub-ensembles of detected quanta, post-selected for each of the joint measurements in a CHSH test, cannot be physically identical. Accordingly, the Peres conjecture (mentioned above) has been rigorously proven, and we can see that—indeed—the strange predictions of quantum mechanics can be interpreted without paradox, even in the case of delayed-choice entanglement swapping. This insight provides a solid conceptual platform in the search for interpretively conclusive experiments regarding the arrow of time in quantum mechanics.

## 3. Experimental Implications

## 4. Proposal

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Spatial filtering of polarization components in optical arrangements. Input modes of polarization can suffer differential phase-shifts during propagation through birefringent media. If the axis of polarization of a component is neither parallel to the fast axis nor to the slow axis of a polarizing beam-splitter, it will suffer a phase shift relative to the rest of the projection. As a result, a single spatial mode at the input can be transformed into a projection with several spatial modes at the output, if it is not polarized. These modes can be resolved in the focal plane of a lens, in which case input polarization information is converted into output spatial information. (

**a**) Optical modes are not perturbed by ideal non-polarizing beam-splitters (NPBS), such as half-silvered mirrors. Component states of polarization cannot be spatially resolved. (

**b**) A single optical mode is transformed into multiple optical modes after passing through a polarizing beam-splitter (PBS). Individual modes can be isolated in the focal plane with a pinhole (or, even better, with the tip of a single-mode optical fiber). The input state of polarization is erased by the birefringent medium, but the relative magnitude of the corresponding spatial mode can be measured and used for post-processing.

**Figure 2.**Coincidence pattern in a four-quantum experiment. If a set of four entangled beams is measured in the same way, the rates of coincidence are expected to be constant for any number of events (2, 3 or 4). If each beam is measured for a different variable, as shown, then two-quantum coincidences are expected to outnumber four-quantum coincidences for sharp measurements. In this case, (a,b) coincidences can be seen in iterations 1, 5, 6 and 7, while quadruple coincidences can only be found in iterations 1 and 6. This is a known trait of relevant experiments, but the theoretical significance of these patterns (as a necessary feature, rather than a technological limitation) was only recently evaluated, as shown in the text.

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