Certifying asymmetry in the configuration of three qubits

Abstract Symmetry restrictions limit the types of tasks that can be achieved with a given set of quantum states. Therefore, any breaking of these symmetries could potentially be exploited as a resource for quantum communication. Here we demonstrate this operationally by certifying asymmetry in the configuration of the Bloch vectors of a set of three unknown qubit states within the dimensionally bounded prepare-and-measure scenario. To do this, we construct a linear witness from three simpler witnesses as building blocks, each featuring, along with two binary measurement settings, three preparations; two of them are associated with the certification task, while the third one serves as an auxiliary. The final witness is chosen to self-test some target configuration. We numerically derive a bound <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mtext>mirror</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> for any mirror-symmetric configuration, thereby certifying asymmetry if this bound is exceeded (e.g. experimentally) for the unknown qubit configuration. We also consider the gap <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mtext>mirror</mml:mtext> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> between the analytically derived overall quantum maximum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mtext>max</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and the mirror-symmetric bound, and use it as a quantifier of asymmetry in the target configuration. Numerical optimization shows that the most asymmetric configuration then forms a right scalene triangle on the unit Bloch sphere. Finally, we implement our protocol on a public quantum processor, where a clear violation of the mirror-symmetric bound certifies asymmetry in the configuration of our experimental triple of qubit states.