Correlating Local Quantum Reality with Causally Disconnected Choices

TL;DR

The paper tackles whether elements of reality in one lab can be correlated with causally disconnected choices, challenging locality-based interpretations of quantum mechanics. It introduces the Reality Quantum Correlator and an operational framework based on the irreality measure $\mathfrak{I}_Q(\rho)$ together with a decomposition into coherence and discord, and it translates these concepts into a concrete optical proposal with atoms inside a Mach-Zehnder interferometer. The authors derive clear predictions: with QWP_in, Bob's path becomes maximally irreal while the atoms lose realism; with QWP_out, Bob's path and the atomic energies are real, and the irreality magnitudes track the initial AB entanglement via entropy terms such as $-\mathfrak{c}^2 \log_2 \mathfrak{c}^2 - \mathfrak{s}^2 \log_2 \mathfrak{s}^2$. An IBMQ demonstration of the circuit implementation and quantum state tomography supports the core claim that Alice's causally disconnected choices correlate with Bob's local reality, while noting a locality loophole and practical noise that call for future optical implementations to close the loophole.

Abstract

In 1935, Einstein, Podolsky, and Rosen (EPR) claimed the incompleteness of quantum mechanics based on the notions of realism (``{\it If, without in any way disrupting a system, we can predict with certainty - i.e., with a probability of one - the value of a physical quantity, then an element of physical reality corresponds to this physical quantity.}'') and locality (``{\it ...\,since the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system}''). EPR also insisted that ``{\it The elements of physical reality cannot be determined by \emph{a priori} philosophical considerations, but must be found by\,...\,experiments and measurements.}''. Here, employing an operational framework for testing realism in quantum systems, we envisage an experiment -- referred to as the Reality Quantum Correlator (RQC) -- capable of showing that the elements of reality in one laboratory can be correlated with causally disconnected choices, thus questioning EPR's locality. Empirical evidence supporting our theoretical predictions is then provided by implementing the corresponding quantum circuit on IBM's quantum computers.

Figures (3)

• Figure 1: Schematic representation of the reality quantum correlator (RQC), an optical setup with atoms 1 and 2 respectively placed in the upper and lower paths of a Mach-Zehnder interferometer (MZI). In this setting, QWP stands for a quarter wave-plate, PBS (as PBS$_{A}$) is a polarizing beam splitter, HWP is a half wave plate, M represents mirrors, BS is a beam splitter, $D_{j,k}$ are detectors (with $j=0,1$ and $k=a,b$, where $a$ ($b$) is the path of the photon $\mathcal{A}$ ($\mathcal{B}$)), and BBO$^{\prime}$ stands for a non-linear crystal of beta barium borate supplemented with auxiliary equipment, through which a pair of photons is produced with their polarizations partially entangled. The $\cal{A}$ and $\cal{B}$ photons go to spacelike separated regions so that they cannot communicate during the time interval needed for the local operations. Photon $\mathcal{A}$ can pass through a QWP and goes through the PBS$_{A}$ while the photon $\mathcal{B}$ goes through an MZI. The dotted blue box represents the two arrangements adopted for implementing the reality correlator: for the QWP$_\text{out}$ (QWP$_\text{in}$) configuration, QWP is out (in) of photon $\cal{A}$'s path and a procedure exists that nonlocally correlates Alice's choices with photon $\cal{B}$'s path and atoms' energies being (not being) elements of the physical reality.
• Figure 2: The quantum circuit implemented in the IBMQ for simulating the reality quantum correlator (RQC). Each blue dotted box is the decomposition into quantum logic gates of the optical devices and the photon-atoms interaction (PAI) explored in the main text. Each horizontal line represents a qubit that is identified with the notation used in the main text, and all qubits are initialized in the state $\ket{0}$. The photons $\mathcal{A}$ and $\mathcal{B}$ possess respective path degrees of freedom, $a$ and $b$, and the polarization degrees of freedom, $A$ and $B$. The barium beta borate plus auxiliary equipment (BBO$^{\prime}$), which is simulated in quantum computers through the action of the RY$(\theta)$ gate on $A$, the CNOT gate having $A$ as control and target in $B$, and the Pauli $X$ gate acting on $B$. After that, the entangled state in the polarization degrees of freedom is given by $\ket{\Psi_+}_{AB} =\mathfrak{c}\ket{01}_{AB} +\mathfrak{s}\ket{10}_{AB}$ with $\mathfrak{c}=\cos(\theta/2)$, $\mathfrak{s}=\sin(\theta/2)$, and $\theta\in[0,\frac{\pi}{2}]$. The photon $\mathcal{B}$ enters the Mach-Zehnder interferometer (MZI) passing first through the polarizing beam splitter (PBS) which, as PBS$_{A}$, is implemented with the gates $C_Z$ and $C_Y$, both with polarization as control and the path as target. Then $\mathcal{B}$ passes through the half-wave plate (HWP), which can be implemented through a CNOT with control in $b$ and target in $B$. The gate $X$ is applied to the qubits $\epsilon_1$ and $\epsilon_2$ to produce the initial excited state of the energy of the atoms $\ket{11}$ considered in our proposal. The photon-atoms interaction (PAI) is constructed using CNOTs, both with control in $b$ and target in $\epsilon_1$ or $\epsilon_2$ (for $\epsilon_1$, though, the gate $X$ has to be applied before and after control in the CNOT, as we want the interaction to occur when the path $b$ is in state $\ket{0}$, corresponding to the upper path of the MZI). The mirrors' (M) combined action is implemented using $U_\text{M}^b = YZ$ and the beam splitter (BS) is simulated with $U_{\text{BS}}^b = SHS$. Finally, the quarter-wave plate (QWP) is implemented via $U_{\text{QWP}}^A = SH$, the device that represents Alice's choice, which can be present (QWP$_{\text{in}}$) or absent (QWP$_{\text{out}}$) in the experimental setup. The dashed vertical lines represent quantum state tomography (QST). The first run, referred to as QST$_b$, was performed when the system is in the state $\ket{\Psi_2^\text{\tiny out(in)}}$. The second run of QST, denoted QST$_{\epsilon_{k}}$, was performed when the state of the system is $\ket{\Psi_5^\text{\tiny out(in)}}$.
• Figure 3: Theoretical (lines) and simulated and demonstrative (points) results for the irreality as a function of $\theta$, the parameter related to the initial polarization entanglement. The simulation results, obtained via classical emulation of the quantum circuit, are denoted by triangular points, whereas the experimental results are given by diamond and square points. (a) Irreality of the photon $\mathcal{B}$ path, $b$, calculated from quantum state tomography applied after the HWP and before $\mathcal{B}$ interacts with the atoms 1 and 2. (b) Irrealities of the atoms' energies ($\mathfrak{I}_{\epsilon_{k}}$) calculated for the quantum state obtained at the MZI output. Both graphs present the results considering the scenarios QWP$_{\text{in}}$ and QWP$_{\text{out}}$. The simulated and experimental points around the solid theoretical line refer to the case where the QWP is inserted in the device (QWP$_{\text{in}}$). The points around the dashed theoretical line are for cases where QWP is not present in the experimental apparatus (QWP$_{\text{out}}$). For $\theta = \pi/2$ (resp. $\theta=0$) the initial entanglement between the polarizations $A$ and $B$ is maximum (resp. zero). The error bars are the standard deviation for ten repetitions of the demonstration. For the demonstrations using IBMQ, we employed the Falcon processor ibm_nairobi quantum chip (its calibration parameters are given in Table \ref{['tab_nairobi']}).