Distinguishing Polarization Mixtures: A New Path To Entanglement-Based Signalling
Using quantum entanglement to send signals between distant parties has long been considered impossible. This page outlines a potential method for doing just that — and explores what may be missing from the standard quantum formalism.
Erik Ayer
Introduction: What I've Done And Why It Matters
Quantum entanglement is a subtle connection that can exist between particles. Certain properties may be in what's called a superposition state — meaning they aren't fixed, but have the potential to become one of several values when measured. With entangled particles, both are in superposition, but their properties are linked: measuring one instantly collapses its state to a definite value — and simultaneously collapses its partner's state to a corresponding value, regardless of distance.In 1935, Einstein and two colleagues described entanglement as evidence that quantum mechanics couldn’t be complete — it seemed to allow instantaneous effects at a distance. Decades later, the 2022 Nobel Prize in Physics was awarded for experiments confirming that entanglement is real, and that its predictions hold.Because the outcome of any individual measurement is random, entanglement has long been thought useless for communication. Only after comparing results from both ends of an experiment do the correlations become visible.The Quantum Eraser is one such experiment: it shows how interference in a double-slit setup can be controlled by a measurement on a distant, entangled photon beam. In this setup, beam A passes through a polarizer. Photons either align with the polarizer and pass through, or are orthogonal and get blocked. The entangled partners in beam B then take on the opposite polarization.If the polarizer in beam A is horizontal, beam B becomes a mixture of horizontal and vertical (H/V) photons. If the polarizer is diagonal, beam B becomes a mixture of diagonal and anti-diagonal (D/A) photons.One of these mixtures leads to two overlapping interference patterns in beam B, which can be reconstructed by filtering for coincident photons that passed through the polarizer in beam A. The other mixture results in no interference.I’ve combined the Quantum Eraser with Afshar’s experiment — originally designed to test the wave-particle duality of light. The result is an optical system that directly distinguishes between different polarization mixtures, without requiring coincidence detection.This potentially opens the door to signaling using entanglement — not just in theory, but in practice. A patent on this method is currently pending.
Quantum Eraser
The source of entangled photons for the Quantum Eraser experiment is a high-powered, short-wavelength laser directed into a nonlinear optical crystal — typically beta-barium borate (BBO). A small fraction of the laser photons (about one in ten billion) undergo spontaneous parametric down-conversion (SPDC), splitting into two longer-wavelength photons.In type-II SPDC, the resulting photons have orthogonal polarizations and emerge in two intersecting cones of light. Where these cones cross, the photons are polarization-entangled in a singlet state: always opposite in polarization, no matter what basis is chosen for measurement.
In schematic form:
The pump beam generates pairs of photons with perfectly anti-correlated polarizations. When the polarizer in beam A is set (say, horizontal), the photons reaching it collapse randomly to either horizontal (H), which pass through, or vertical (V), which are blocked. The same applies when the polarizer is diagonal.At this point, entanglement is complete — both photons have collapsed into definite, unentangled states.Now consider what happens to beam B if it passes through a standard double-slit. You’ll get an interference pattern regardless of whether it’s a mixture of H/V or D/A polarized light.
But that changes if you introduce quarter-wave plates (QWPs) in front of the slits.
QWPs are birefringent materials: they delay one polarization axis relative to the orthogonal one. Their thickness is tuned to delay the "slow" axis by one-quarter wavelength compared to the "fast" axis.Horizontally or vertically polarized light passes through without its polarization being altered, but gets delayed differently at each slit.One slit’s QWP has its fast axis horizontal, the other vertical.This causes the interference patterns for H and V light to shift by ¼ of a fringe spacing in opposite directions.When summed together, the patterns cancel out the interference, resulting in a smooth Gaussian intensity envelope — the interference is hidden.Now, consider diagonally polarized light, which is a superposition of H and V.The QWPs act on the H and V components separately.One component is delayed, converting the linear polarization into circular polarization.The result is either left- or right-circular polarization, depending on the QWP orientation.Since the two slits apply opposite circular polarizations, the photons become distinguishable, and no interference is possible.
Depending on the orientation of the light's polarization with respect to the fast and slow axes of the QWP, the resulting circular polarization can be left-circular or right-circular. since the two QWP are rotated 90 degrees from each other, the wave going through each slit has a different circular polarization, and this prevents it from interfering.
Since one one of the two possible polarizations makes it through the polarizer in beam A, detecting photons in beam B in coincidence with the surviving photons in beam A will pick out just one of the interference patterns (or lack of interference for diagonal polarizer).
This experiment demonstrates that interference can be controlled by making a measurement on a beam of entangled photons. This is a nonlocal effect, as the measurement on one photon affects the observed behavior of its entangled partner without any direct physical connection between the two beams.However, because horizontal and vertical polarizations each produce their own shifted interference patterns, it is necessary to filter out one of them using coincidence detection — only registering photons in one beam when their entangled partners are also detected in the other. This reliance on coincidence makes the setup unsuitable for communication, as it requires classical post-processing to see the effect.
Afshar's Experiment
In the early 2000s, Shahriar Afshar performed and experiment that challenged the usual interpretation of wave-particle duality. In the classic double-slit experiment, light behaves like a wave when not observed, creating and interference pattern and like a particle when the path is known. The standard view is that you can't know which path a photon took and get an interference pattern - this is the principle of complementarity.Afshar's setup tested this directly.First, light passed through two slits and formed an interference pattern. Afshar placed thin wires exactly where the dark fringes of the interference pattern occurred. Because there was no light at these positions, the wires didn’t disturb the light significantly. After the wires, a lens refocused the beams onto two detectors corresponding to the original slits — supposedly revealing “which-path” information.Despite the presence of this which-path information, the wires did not block or scatter significant light. This suggested that interference was still present — even though path information could theoretically be obtained. Afshar claimed this meant both wave and particle behavior were visible at once, challenging Bohr's complementarity principle.
Afshar's results are still debated, but the key insight for our purposes is this: the interference pattern doesn't need to be directly seen - its absence can be inferred by how well the light avoids obstacles placed at the dark fringes.
Combining The Quantum Eraser And Afshar's Experiment
The Quantum Eraser shows that interference in one entangled beam can be controlled by a measurement performed on its partner. However, for horizontally and vertically polarized light (H/V), there are two shifted interference patterns. These overlap and combine to form a smooth Gaussian brightness profile, erasing visible interference unless one is filtered out using coincidence detection.But this filtering can also be done physically.Afshar’s experiment demonstrated that interference can be inferred indirectly: by placing wires at the dark fringes of an interference pattern, he showed that the light still passed through without being blocked — unless the interference was disturbed. These wires acted as a non-invasive test for whether interference was present.By placing such wires at the dark fringes of just one polarization’s interference pattern — say, the H-polarized one — we can selectively block that component. Then, if the input is a mixture of H and V, the wires block H-polarized light, creating an imbalance in polarization. If the input is a mixture of diagonal and anti-diagonal (D/A) polarizations, there is *no interference, so light from both components gets blocked equally, resulting in no imbalance.This subtle difference allows us to distinguish between the two mixtures.A lens (as in Afshar’s experiment) then focuses the light into two slit images. Each image still contains both polarizations, but if we place polarizing filters in front of each image — horizontal for one, vertical for the other — an imbalance in brightness emerges for H/V input. For D/A input, the light is circularly polarized (after the QWPs), and each polarizer passes half the light. The two images are equally bright.
Simulation Results
I wrote a Python script to simulate interference, focus with a lens, allow for blocks, and have two sensors to integrate rays. I takes interference effects into account and applied them to each ray at the position of the lens.The beam blocks are placed, roughtly, in the interference fringes from horizontally polarized light. The sensors have horizontal and vertical polarizers, so rays compute a dot product with those to get the intensity that reaches the sensor.The following graphs have H/V with an extra rotation applied to both. Graphs with 0, 15, 30, and 45 degrees of rotation are shown. Play close attention to the ratio of light between the detectors.
The ratio changes with the rotation of the two polarizations. The density matricies for all of these combinations of polarization are the same, from standard quantum mechanics, so there should be no possible experiment that can distinguish them. However, this simulation (as well as my experimental results), show that at least the interpretation of standard quantum mechanics misses something.Here is a link to my code on GitHub:
Optical System
Rebuilding this to work better.