Discrete phase-space structure of nn-qubit mutually unbiased bases

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field \Gal{2^n} and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.Comment: Title changed. Improved version. Accepted for publication in Annals of Physic

Unpolarized states and hidden polarization

We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of \textit{hidden} polarisation emerges in a natural way in this context.Comment: 7 pages, 3 eps-color figures. Submitted to PRA. Comments welcome

Redemptive Strategies in the Novels of Bernard Malamud

In an interview with critic Robert Kegan, Bernard Malamud spoke about his characters: What strikes me about them,” he said, “is that all throughout they have possibilities. They have opportunities to leave. They have a way out, but they never give up.” “My belief, Malamud said, is in human possibility”. As an experimenter with the novel form, Malamud has written seven novels, each uniquely different in style and genre, and yet each expressing this vision of human possibility. The main characters in his novels possess within themselves the potential to overcome their self-doubts and moral indiscretions. When they do, they assume a new life based on the time-honored value of service to others with love and compassion. When they fail, they become static reminders of Malamud\u27s belief that a life without human service and commitment is a life devoid of meaning and purpose. These human possibilities for growth and commitment are played out in a world which is rife with human suffering and deprivation. From the poor neighborhoods of The Assistant\u27s New York City to the fabled wastelands of God\u27s Grace\u27s nuclear devastation, Malamud\u27s characters shuffle through their lives isolated from humanity and beleaguered by circumstance. They are frequently, as Samuel Weiss says, . Jews without money, anxious, luckless, and frustrated, and engaged in a fundamental struggle to survive or to find and fix a purpose in life . In the Yiddish vernacular, they are known as schlemiels, holy innocents, who, in spite of hard luck and bad breaks, have managed to survive and grow both morally and spiritually. Ruth Wisse comments that in literature a schlemiel is above all a reaction against the evil surrounding him…

Quality of a Which-Way Detector

We introduce a measure Q of the "quality" of a quantum which-way detector, which characterizes its intrinsic ability to extract which-way information in an asymmetric two-way interferometer. The "quality" Q allows one to separate the contribution to the distinguishability of the ways arising from the quantum properties of the detector from the contribution stemming from a-priori which-way knowledge available to the experimenter, which can be quantified by a predictability parameter P. We provide an inequality relating these two sources of which-way information to the value of the fringe visibility displayed by the interferometer. We show that this inequality is an expression of duality, allowing one to trace the loss of coherence to the two reservoirs of which-way information represented by Q and P. Finally, we illustrate the formalism with the use of a quantum logic gate: the Symmetric Quanton-Detecton System (SQDS). The SQDS can be regarded as two qubits trying to acquire which way information about each other. The SQDS will provide an illustrating example of the reciprocal effects induced by duality between system and which-way detector.Comment: 10 pages, 5 figure

Uncertainty reconciles complementarity with joint measurability

The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question.Comment: 4 pages, RevTeX. Title of previous version: "Complementarity and uncertainty - entangled in joint path-interference measurements". This new version focuses on the "measurement uncertainty relation" and its role, disentangling this issue from the special context of path interference duality. See also http://www.vjquantuminfo.org (October 2003

Recency-sensitive retrieval processes in long-term free recall

In several experiments, each presentation of a to-be-remembered item in a free-recall list was both preceded and followed by a distracting activity and recall was delayed by an additional period of distracting activity. Pronounced long-term effects of recency were obtained, the standard short-term memory interpretation of recency effects in free recall notwithstanding. The results are interpreted as reflecting retrieval processes that are obscured by procedural characteristics of typical free-recall experiments.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22374/1/0000823.pd

Adolescents, Adults and Rewards: Comparing Motivational Neurocircuitry Recruitment Using fMRI

Background: Adolescent risk-taking, including behaviors resulting in injury or death, has been attributed in part to maturational differences in mesolimbic incentive-motivational neurocircuitry, including ostensible oversensitivity of the nucleus accumbens (NAcc) to rewards. Methodology/Principal Findings: To test whether adolescents showed increased NAcc activation by cues for rewards, or by delivery of rewards, we scanned 24 adolescents (age 12–17) and 24 adults age (22–42) with functional magnetic resonance imaging while they performed a monetary incentive delay (MID) task. The MID task was configured to temporally disentangle potential reward or potential loss anticipation-related brain signal from reward or loss notification-related signal. Subjects saw cues signaling opportunities to win or avoid losing $0,$.50, or $5 for responding quickly to a subsequent target. Subjects then viewed feedback of their trial success after a variable interval from cue presentation of between 6 to17 s. Adolescents showed reduced NAcc recruitment by reward-predictive cues compared to adult controls in a linear contrast with non-incentive cues, and in a volume-of-interest analysis of signal change in the NAcc. In contrast, adolescents showed little difference in striatal and frontocortical responsiveness to reward deliveries compared to adults. Conclusions/Significance: In light of divergent developmental difference findings between neuroimaging incentive paradigms (as well as at different stages within the same task), these data suggest that maturational differences i