Device-independent prepare-and-prepare bipartite null witness dimension test with a single joint measurement

We propose a device-independent null witness dimensionality test with bipartite measurements and input from two separate parties. The dimension is determined from the rank of the matrix of measurements for pairs of states prepared by the parties. We have applied the test to various IBM Quantum devices. The results demonstrate extreme precision of the test, which is able to detect disagreements with the qubit (two-level) space of bipartite measurement even in the presence of technical imperfections. The deviations beyond 6 standard deviations have no simple origin and need urgent explanations to unblock progress in quantum computing.

💡 Research Summary

This paper introduces a novel device-independent protocol for testing the dimensionality of a bipartite quantum system, termed the Prepare-and-Prepare (PP) scenario. The test requires two independent parties, A and B, each preparing their local subsystem in one of n predefined states. Subsequently, a single, fixed joint measurement is performed on the composite system. The core idea is to construct an n×n probability matrix p, where each entry p_ij is the probability of a specific measurement outcome given that party A prepared state i and party B prepared state j. The rank of this matrix is fundamentally limited by the dimensions of the local state spaces prepared by A and B. Consequently, the determinant W_n = det(p) serves as a null witness: if the actual system dimension (Schmidt number) is lower than a certain threshold relative to n, theory dictates that W_n should be zero (within statistical error). A statistically significant non-zero value signals a violation of the assumed dimensionality.

To maximize the test’s sensitivity, the authors select the set of local prepared states to lie on the Viviani curve on the Bloch sphere, ensuring they span a non-planar, three-dimensional set of vectors in the Bloch representation, thus providing a stringent test for a two-level qubit space. The experimental measurement protocol is cleverly designed to enhance device independence. It employs a third “referee” qubit (M) that is measured, separating the final measurement from the qubits used for state preparation (A and B). A specific sub-circuit, involving CNOT gates and single-qubit rotations, maps the desired joint measurement operator onto the standard computational basis measurement of qubit M.

The proposed test was implemented on various IBM Quantum processors. Results demonstrated the test’s extreme precision and robustness to common technical imperfections like gate errors. On several devices, especially newer Heron-based systems, the measured W_5 value was consistent with zero, confirming operation within a two-dimensional qubit space. However, the most striking finding was observed on some devices (e.g., ibm_kyiv), where the deviation of W_5 from zero exceeded six standard deviations. This significant discrepancy cannot be easily attributed to simple noise sources or calibration errors. It suggests that the effective physical Hilbert space of the implemented qubits might deviate from the ideal two-level model, a possibility with serious implications for quantum error correction and mitigation strategies that typically assume a well-defined qubit subspace.

The paper provides detailed appendices covering the mathematical construction of the witness, the explicit form of quantum gates used, the full circuit transformations, and tabulated theoretical maximum values for W_n under different dimensionality assumptions. In conclusion, this work presents a powerful and precise new tool for the device-independent verification of quantum processor dimensionality. Its application has uncovered anomalous behavior in current hardware that warrants urgent further investigation to ensure reliable progress in quantum computing.