Quantum observable's reality erasure with spacelike-separated operations

TL;DR

The paper addresses whether Alice’s spacelike-separated operations can erase the spatial reality of Bob’s observables, reframing realism through the quantum irrealism measure $\mathfrak{I}_X(\rho)$. It introduces a nonlocal quantum reality eraser implemented with entangled photons and an extended setup that includes two extra degrees of freedom $d_{1,2}$, allowing reality erasure to be diagnosed via irreality rather than visibility. Theoretical predictions link irreality to the initial entanglement and show that $\mathfrak{I}_b$ vanishes for certain configurations while $\mathfrak{I}_{d_{1,2}}$ becomes nonzero when erasure is induced, all demonstrated experimentally with quantum state tomography in spacelike-separated labs. The results provide strong evidence against local realism and extend quantum eraser concepts by operationalizing irrealism and nonlocality through extra degrees of freedom, though the precise quantum resource enabling the effect remains to be clarified.

Abstract

In 1935, Einstein, Podolsky, and Rosen argued that quantum mechanics is incomplete based on the assumption that local actions cannot influence elements of reality at a distant location (local realism). In this work, using a recently defined quantum reality quantifier, we show that Alice's local quantum operations can be correlated with the erasure of the reality of observables in Bob's causally disconnected laboratory. To this end, we implement a modified optical quantum eraser experiment, ensuring that Alice's and Bob's measurements remain causally disconnected. Using an entangled pair of photons and quantum state tomography, we experimentally verify that, even with the total absence of any form of classical communication, the choice of quantum operation applied by Alice on her photon is correlated with the erasure of a spatial element of reality of Bob's photon. Our results reveal that Bob's photon can entangle two extra non-interacting degrees of freedom, thus confirming that Bob's photon path is not an element of physical reality.

Figures (5)

• Figure 1: Schematic of the reality quantum eraser. A pair of entangled photons is generated through beta-barium-borate crystals (correlation source), with one photon directed to Alice's site and the other to Bob's, where two d.o.f., $d_{1,2}$, have been prepared as EORs (solid red bullets), that is, $\mathfrak{I}_{d_{1,2}}=0$. Alice submits her photon to one of two configurations, $\mathscr{C}_{z(x)}$, and then measures the photon's path, assigning it an EOR (blue bullets on Alice's side). When Alice chooses the configuration $\mathscr{C}_z$ ($\mathscr{C}_x$) and measures her photon, Bob's photon acquires a spatial EOR (enters in path superposition), interacts with either $d_1$ or $d_2$ (interacts with both $d_{1,2}$), and leaves these d.o.f. correlated (entangled). Theoretical predictions show that, when $\mathscr{C}_x$ is chosen, the $d_{1,2}$ EORs are found erased after Alice's photon is measured, that is, $\mathfrak{I}_{d_{1,2}}>0$, even when the sites are spacelike separated.
• Figure 2: A photon pair source located in the middle produced polarization-entangled photons at center wavelengths of $650\;\text{nm}$. These photons were then routed through optical fibers and transmitted to separate laboratories belonging to Bob and Alice, situated $45\;\text{m}$ apart from each other. The inset (d) shows the space-time location of the events corresponding to Alice's (red point) and Bob's (blue point) measurements in the performed experiments. Thus, Alice's quantum operations are space-like separated from Bob's measurements. Alice is free to decide whether to insert HWP$_\text{A}$ into the photon’s path before directing it to PBS$_\text{A}$. In Bob's laboratory there is a Sagnac interferometer with the clockwise ($\ket{0}_b$) and counterclockwise ($\ket{1}_b$) path accessed, respectively, by photons transmitted and reflected in the PBS. The beam-displacer BD$_1$ (BD$_2$) introduces an extra d.o.f. $d_1$ ($d_2$) in the $\ket{1}_b$ ($\ket{0}_b$) path. The sets P$_{\text{in}}$, P'$_{\text{in}}$ and BD$_\text{T}$ constitute the apparatuses used to perform the quantum state tomography related to $d_{1,2}$, while the sets PBS$_\text{T}$ and P$_{\text{out}}$ perform the quantum state tomography related to $b$. The measurements are performed utilizing avalanche photodetectors with a coincidence acquisition device.
• Figure 3: Theoretical (solid and dashed lines) and experimental (points) results for the irreality as a function of $\theta$, the parameter related to the initial polarization entanglement; the higher $\theta$ the stronger the entanglement. (a) Irreality $\mathfrak{I}_b$ of the photon path $b$ calculated from quantum state tomography applied before Bob's photon interacts with BD$_{1,2}$. (b) Irrealities $\mathfrak{I}_{d_{1,2}}$ the d.o.f. $d_{1,2}$, with $\mathfrak{I}_{d_1}=\mathfrak{I}_{d_2}$, calculated for the quantum state obtained after the interaction with the BD$_{1,2}$. In plots (a) and (b), the dashed line and the corresponding data points represent the scenario in which Alice selects the $\mathscr{C}_z$ configuration. Conversely, the solid line and the corresponding data points represent the $\mathscr{C}_x$ configuration.
• Figure 4: Density matrices of the Hilbert space $\{b,d_1,d_2\}$ obtained for different values of $\theta$. The blue dashed circles in the graph of $\mathfrak{I}_{d_{1,2}}$ indicate the corresponding points for each density matrix. The left (right) column corresponds to the matrices obtained when Alice implements projections onto $\ket{+}$ ($\ket{0}$).
• Figure 5: (a) Usual structure of a Mach-Zehnder interferometer, with two beam-splitters (BS), two mirrors (M), a phase shifter (PS), and two detectors (D$_{0,1}$). (b) Two degrees of freedom (d.o.f.) $d_{1,2}$ are placed in the arms of the MZI so as to mark the path taken by $Q$.