Quantum Multi-Prover Interactive Proof Systems with Limited Prior Entanglement

This paper gives the first formal treatment of a quantum analogue of multi-prover interactive proof systems. It is proved that the class of languages having quantum multi-prover interactive proof systems is necessarily contained in NEXP, under the assumption that provers are allowed to share at most polynomially many prior-entangled qubits. This implies that, in particular, if provers do not share any prior entanglement with each other, the class of languages having quantum multi-prover interactive proof systems is equal to NEXP. Related to these, it is shown that, in the case a prover does not have his private qubits, the class of languages having quantum single-prover interactive proof systems is also equal to NEXP.Comment: LaTeX2e, 19 pages, 2 figures, title changed, some of the sections are fully revised, journal version in Journal of Computer and System Science

Quantum Model of Human Subjectivity for Moral Psychology: Using Q Methodology to Define Features of Judgments in Hilbert Space

A major issue in the field of moral psychology is identifying aspects of human morality that can be measured. Kantor's (1959) formulation of a psychological event provides a unique option for the field. A psychological event evolves over time through the interaction of current situations and stimuli with historical interbehavioral processes. Kantor's formulation of a psychological event has these elements interacting within the psychological field under review, but the space is undefined. Stephenson (1982) offers Q methodology as a research tool to measure psychological events and does so by defining the psychological field within Hilbert space梐 generalized Euclidean space where belief states of individuals are represented as vectors within the space. Using the well-known Julie and Mark vignette (Haidt, 2001) about a sister and brother who decide to make love, this study investigates the viewpoints of participants, who are experts in moral philosophy and psychology, regarding the story. In previous studies with the Julie and Mark vignette, participants were unable to articulate their beliefs about the event: this has led to the conclusion that people have intuitive moral reactions, but they often exhibit dumbfounding when they attempt to explain their intuitive reactions (Haidt, 2001). This Q methodology study operationalized the subjective perspectives of participants in order to define their viewpoints. The stable viewpoints are defined with the data and show unique ways of framing the story and are Personal Autonomy, Human Nature, Outcomes, and Individuals in Context. The interpretation of the findings defines these viewpoints and shows how they differ when the vignette is considered from different perspectives. By setting the psychological field within Hilbert space where quantum theory explicitly applies (Stephenson, 1982), the viewpoints can be used to define the features of belief projections as explained by the important work in quantum cognition and decision making. By defining participants' viewpoints, this study shows that people are not dumbfounded about their moral beliefs.Educational Psycholog