Generalized self-testing and the security of the 6-state protocol

Self-tested quantum information processing provides a means for doing useful information processing with untrusted quantum apparatus. Previous work was limited to performing computations and protocols in real Hilbert spaces, which is not a serious obstacle if one is only interested in final measurement statistics being correct (for example, getting the correct factors of a large number after running Shor's factoring algorithm). This limitation was shown by McKague et al. to be fundamental, since there is no way to experimentally distinguish any quantum experiment from a special simulation using states and operators with only real coefficients. In this paper, we show that one can still do a meaningful self-test of quantum apparatus with complex amplitudes. In particular, we define a family of simulations of quantum experiments, based on complex conjugation, with two interesting properties. First, we are able to define a self-test which may be passed only by states and operators that are equivalent to simulations within the family. This extends work of Mayers and Yao and Magniez et al. in self-testing of quantum apparatus, and includes a complex measurement. Second, any of the simulations in the family may be used to implement a secure 6-state QKD protocol, which was previously not known to be implementable in a self-tested framework.Comment: To appear in proceedings of TQC 201

Quantum information cannot be split into complementary parts

We prove a new impossibility for quantum information (the no-splitting theorem): an unknown quantum bit (qubit) cannot be split into two complementary qubits. This impossibility, together with the no-cloning theorem, demonstrates that an unknown qubit state is a single entity, which cannot be cloned or split. This sheds new light on quantum computation and quantum information.Comment: 9 pages, 1 figur

Simulating quantum systems using real Hilbert spaces

We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends previous results which were unable to simulate local evolution and measurements with local operators and was limited to discrete evolution. We also detail applications to Bell inequalities and self-testing of quantum apparatus.Comment: 4 page

Device-independent dimension test in a multiparty Bell experiment

A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions concerning the quantum apparatus. Previous work mostly deals with the two-party version of this problem. In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment. Our dimension test stems from the study of a new multiparty scenario which we call prepare-and-distribute. This is like the prepare-and-measure scenario, but the quantum state is sent to multiple, non-communicating parties. Through specific examples, we show that our test results can be tight. Furthermore, we compare the performance of our test to results based on known bipartite tests, and witness remarkable advantage, which indicates that our test is of a true multiparty nature. We conclude by pointing out that with some partial information about the quantum states involved in the experiment, it is possible to learn other interesting properties beyond dimension.Comment: 10 pages, 2 figure