Complementarity between entanglement-assisted and quantum distributed random access code

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of $3\to 1$ distributed RACs [J. Bowles, N. Brunner, and M. Pawłowski, Phys. Rev. A 92, 022351 (2015)] and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa. Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the $3\to 1$ distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.

Figure 1

The encoding quantum states given by Eq. (1) in the Bloch sphere for input $x_0{x}_1{x}_2$ for the standard $3\to 1$ RAC.

Figure 2

$3\to 1$ distributed RACs with three different resources are shown. The first two devices receive inputs $x_0,x_1$, and $x_2$ (where $x_i\in \{0,1\}$), respectively. The third device receives input $y\in \{0,1,2\}$ and provides an answer $z$. All classical (double line) or quantum (thick line) communication channels between devices are restricted to two-dimensional systems. In (a), $\mathcal{CR}$ denotes that the devices can share classical randomness. In (b), ${|\mathrm{\Phi }\rangle }_i$ represents the $i\mathrm{th}$ qubit of the entangled GHZ state shared among the devices. In the distributed EARAC, the first two devices measure the respective shared qubits in two different measurement settings depending on $x_0\oplus x_1$ and $m_1\oplus x_2$, and obtain binary measurement outcome $a$ and $b$, respectively. For different guessing functions $f(x,y)$, the explicit forms of these measurements differ, while the third device always chooses the mutually unbiased bases ${\sigma }_Y,{\sigma }_X,{\sigma }_Z$ for $y=0,1,2$. In (c), the first device prepares a qubit according to $x_0,x_1$ and sends it to the second device. For $x_2=1$, the second device applies a unitary $U$ on that qubit, and the third one always measures the qubit in one of the mutually unbiased bases ${\sigma }_Y,{\sigma }_X,{\sigma }_Z$. The encoding quantum states and the unitary operation $U$ are different for different guessing functions $f(x,y)$.

Figure 3

Experimental setup for $3\to 1$ distributed QRAC. Alice encodes her states in horizontal and vertical single-photon polarization states that are prepared by suitable orientation of HWP($\alpha$) and the combination of QWP(${\theta }_1$), HWP($\beta$), QWP(${\theta }_2$). Unitary rotations by Bob along the $x$ axis, $z$ axis, and $\mathbb{1}$ transformation are implemented by a combination of QWP(${\theta }_3$), HWP($\gamma$), and QWP(${\theta }_4$), respectively. A combination of HWP, QWP, and PBS followed by two single-photon detectors $D_i$ ($i=1,2$) allow Charlie to perform the measurements in ${\sigma }_Y,{\sigma }_X,{\sigma }_Z$ bases, respectively.