On the Possibility of Classical Client Blind Quantum Computing

Classical client remote state preparation (CC − RSP) is a primitive where a fully classical party (client) can instruct the preparation of a sequence of random quantum states on some distant party (server) in a way that the description is known to the client but remains hidden from the server. This primitive has many applications, most prominently, it makes blind quantum computing possible for classical clients. In this work, we give a protocol for classical client remote state preparation, that requires minimal resources. The protocol is proven secure against honest-but-curious servers and any malicious third party in a game-based security framework. We provide an instantiation of a trapdoor (approximately) 2-regular family of functions whose security is based on the hardness of the Learning-With-Errors problem, including a first analysis of the set of usable parameters. We also run an experimentation on IBM’s quantum cloud using a toy function. This is the first proof-of-principle experiment of classical client remote state preparation.

The joint distribution of the marginals of multipartite random quantum states

We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the marginals are asymptotically free. We connect the matrix integrals relevant to the study of operators on tensor product spaces with the corresponding classes of combinatorial maps, for which we develop the combinatorial machinery necessary for the asymptotic study. Finally, we present some applications to the theory of random quantum states in quantum information theory.

On the Separability of Unitarily Invariant Random Quantum States: The Unbalanced Regime

We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.

Detecting Violation of Bell Inequalities using LOCC Maximized Quantum Fisher Information and Entanglement Measures

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.