Gelo Noel Tabia

As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation where the nonlocality in two bipartite subsystems forces the remaining bipartite subsystem to exhibit nonlocality. This intriguing effect, dubbed nonlocality transitivity, was first identified in the non-quantum non-signaling world in 2011. However, whether such transitivity could manifest within quantum theory has remained unresolved—until now. Here, we provide the first affirmative answer to this open problem at the level of quantum states, thereby showing that there exists a quantum-realizable notion of nonlocality transitivity. Specifically, by leveraging the possibility of Bell-inequality violation by tensoring, we analytically construct a pair of nonlocal bipartite states such that simultaneously realizing them in a tripartite system induces nonlocality in the remaining bipartite subsystem. En route to showing this, we also prove that multiple copies of the W-state marginals uniquely determine the global compatible state, thus establishing another instance when the parts determine the whole. Surprisingly, the nonlocality transitivity of quantum states also occurs among the reduced states of Haar-random three-qutrit pure states. We further show that the transitivity of quantum steering can already be demonstrated with the marginals of a three-qubit W state, showing again another noteworthy difference between the two forms of quantum correlations. Finally, we present a simple method to construct quantum states and correlations that are nonlocal in all their non-unipartite marginals, which may be of independent interest.

We present recursive schemes for implementing quantum Fourier transforms and inversion about the mean in Grover's algorithm using integrated linear optics with path encoded states. Formally, translating a unitary operation into a linear optical network involves a matrix factorization of the unitary matrix into block-diagonal matrices with a maximum block size of 2. By recursive, we mean that a unitary transformation on 2d modes is realized by using a pair of copies of the same operation on d modes. To demonstrate that our recursive circuits are viable in practice, we ran simulations of proof-of-principle experiments using a fabrication model that accounts for realistic sources of errors in silicon-based photonic integrated devices. We found high-fidelity performance for our optical multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on 4-item and 8-item databases.