Quantum mechanical measurement of non-orthogonal states and a test of non-locality

Arthur Mehta

Quantum graph theory, also known as non-commutative graph theory, is an operator space generalization of graph theory. The independence number, and Lovasz theta function were generalized to this setting by Duan, Severini, and Winter [DSW13] and two different version of the chromatic number were introduced by Stahlke [Sta16] and Paulsen [HPP16]. We introduce two new generalizations of the chromatic number to non-commutative graphs and provide an upper bound on the parameter of Stahlke. We provide a generalization of the graph complement and show the chromatic number of the orthogonal complement of a non-commutative graph is bounded below by its theta number. We also provide a generalization of both Sabidussi's Theorem and Hedetniemi's conjecture to non-commutative graphs. The study of non-local games considers scenarios in which separated players collaborate to provide satisfying responses to questions given by a referee. The condition of separating players makes non-local games an excellent setting to gain insight into quantum phenomena such as entanglement and non-locality. Non-local games can also provide protocols known as self-tests. Self-testing allows an experimenter to interact classically with a black box quantum system and certify that a specific entangled state was present and a specific set of measurements were performed. The most studied self-test is the CHSH game which certifies the presence of a single EPR entangled state and the use of anti-commuting Pauli measurements. We introduce an algebraic generalization of CHSH and obtain a self-test for non-Pauli operators resolving an open question posed by Coladangelo and Stark (QIP 2017). Our games also provide a self-test for states other than the maximally entangled state, and hence resolves the open question posed by Cleve and Mittal (ICALP 2012). This thesis is primarily based on two collaborative works written by the author and several coauthors [CMMN20], [KM19].

Sandu Popescu, Nicolas Gisin

Atanu Bhunia, Saronath Halder, Preeti Parashar +1 more

A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.

Michael J. W. Hall

Dan Cristian Marinescu, Gabriela M. Marinescu

Alessio Serafini, Alex Retzker, Martin Bodo Plenio

We present a detailed study on the possibility of manipulating quantum information encoded in the 'radial' modes of arrays of trapped ions (i.e. in the ions' oscillations orthogonal to the trap's main axis). In such systems, because of the tightness of transverse confinement, the radial modes pertaining to different ions can be addressed individually. In the first part of the paper we show that, if local control of the radial trapping frequencies is available, any linear optical and squeezing operation on the locally defined modes—on single as well as on many modes—can be reproduced by manipulating the frequencies. Then, we proceed to describe schemes apt to generate unprecedented degrees of bipartite and multipartite continuous variable (CV) entanglement under realistic noisy working conditions and even restricting only to a global control of the trapping frequencies. Furthermore, we consider the transmission of the quantum information encoded in the radial modes along the array of ions, and show it to be possible to a remarkable degree of accuracy, for both finite-dimensional and CV quantum states. Finally, as an application, we show that the states which can be generated in this setting allow for the violation of multipartite non-locality tests, by feasible displaced parity measurements. Such a demonstration would be a first test of quantum non-locality for 'massive' degrees of freedom (i.e. for degrees of freedom describing the motion of massive particles).