Dissonance as a resource for probing the qubit depolarizing channel

Quantum channel identification, a standard problem in quantum metrology, is the task of estimating parameter(s) of a quantum channel. We investigate dissonance (quantum discord in the absence of entanglement) as an aid to quantum channel identification and find evidence for dissonance as a resource for quantum information processing. We consider the specific case of dissonant Bell-diagonal probes of the qubit depolarizing channel, using quantum Fisher information as a measure of statistical information extracted by the probe. In this setting dissonant quantum probes yield more statistical information about the depolarizing probability than do corresponding probes without dissonance and greater dissonance yields greater information. This effect only operates consistently when we control for classical correlation between the probe and its ancilla and the joint and marginal purities of the ancilla and probe.

Mental reversal of imagined melodies: A role for the posterior parietal cortex

Two fMRI experiments explored the neural substrates of a musical imagery task that required manipulation of the imagined sounds: temporal reversal of a melody. Musicians were presented with the first few notes of a familiar tune (Experiment 1) or its title (Experiment 2), followed by a string of notes that was either an exact or an inexact reversal. The task was to judge whether the second string was correct or not by mentally reversing all its notes, thus requiring both maintenance and manipulation of the represented string. Both experiments showed considerable activation of the superior parietal lobe (intraparietal sulcus) during the reversal process. Ventrolateral and dorsolateral frontal cortices were also activated, consistent with the memory load required during the task. We also found weaker evidence for some activation of right auditory cortex in both studies, congruent with results from previous simpler music imagery tasks. We interpret these results in the context of other mental transformation tasks, such as mental rotation in the visual domain, which are known to recruit the intraparietal sulcus region, and we propose that this region subserves general computations that require transformations of a sensory input. Mental imagery tasks may thus have both task or modality-specific components as well as components that supersede any specific codes and instead represent amodal mental manipulation.

Behavioral and neural correlates of perceived and imagined musical timbre

The generality of findings implicating secondary auditory areas in auditory imagery was tested by using a timbre imagery task with fMRI. Another aim was to test whether activity in supplementary motor area (SMA) seen in prior studies might have been related to subvocalization. Participants with moderate musical background were scanned while making similarity judgments about the timbre of heard or imagined musical instrument sounds. The critical control condition was a visual imagery task. The pattern of judgments in perceived and imagined conditions was similar, suggesting that perception and imagery access similar cognitive representations of timbre. As expected, judgments of heard timbres, relative to the visual imagery control, activated primary and secondary auditory areas with some right-sided asymmetry. Timbre imagery also activated secondary auditory areas relative to the visual imagery control, although less strongly, in accord with previous data. Significant overlap was observed in these regions between perceptual and imagery conditions. Because the visual control task resulted in deactivation of auditory areas relative to a silent baseline, we interpret the timbre imagery effect as a reversal of that deactivation. Despite the lack of an obvious subvocalization component to timbre imagery, some activity in SMA was observed, suggesting that SMA may have a more general role in imagery beyond any motor component.

Identification, discrimination, and selective adaptation of simultaneous musical intervals

Four experiments investigated perception of major and minor thirds whose component tones were sounded simultaneously. Effects akin to categorical perception of speech sounds were found. In the first experiment, musicians demonstrated relatively sharp category boundaries in identification and peaks near the boundary in discrimination tasks of an interval continuum where the bottom note was always an F and the top note varied from A to A flat in seven equal logarithmic steps. Nonmusicians showed these effects only to a small extent. The musicians showed higher than predicted discrimination performance overall, and reaction time increases at category boundaries. In the second experiment, musicians failed to consistently identify or discriminate thirds which varied in absolute pitch, but retained the proper interval ratio. In the last two experiments, using selective adaptation, consistent shifts were found in both identification and discrimination, similar to those found in speech experiments. Manipulations of adapting and test showed that the mechanism underlying the effect appears to be centrally mediated and confined to a frequency-specific level. A multistage model of interval perception, where the first stages deal only with specific pitches may account for the results.

Hearing in the mind's ear: A PET investigation of musical imagery and perception

Neuropsychological studies have suggested that imagery processes may be mediated by neuronal mechanisms similar to those used in perception. To test this hypothesis, and to explore the neural basis for song imagery, 12 normal subjects were scanned using the water bolus method to measure cerebral blood flow (CBF) during the performance of three tasks. In the control condition subjects saw pairs of words on each trial and judged which word was longer. In the perceptual condition subjects also viewed pairs of words, this time drawn from a familiar song; simultaneously they heard the corresponding song, and their task was to judge the change in pitch of the two cued words within the song. In the imagery condition, subjects performed precisely the same judgment as in the perceptual condition, but with no auditory input. Thus, to perform the imagery task correctly an internal auditory representation must be accessed. Paired-image subtraction of the resulting pattern of CBF, together with matched MRI for anatomical localization, revealed that both perceptual and imagery. tasks produced similar patterns of CBF changes, as compared to the control condition, in keeping with the hypothesis. More specifically, both perceiving and imagining songs are associated with bilateral neuronal activity in the secondary auditory cortices, suggesting that processes within these regions underlie the phenomenological impression of imagined sounds. Other CBF foci elicited in both tasks include areas in the left and right frontal lobes and in the left parietal lobe, as well as the supplementary motor area. This latter region implicates covert vocalization as one component of musical imagery. Direct comparison of imagery and perceptual tasks revealed CBF increases in the inferior frontal polar cortex and right thalamus. We speculate that this network of regions may be specifically associated with retrieval and/or generation of auditory information from memory.

Quantum Energy Teleportation Between Spin Particles in a Gibbs State

Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance-quantum correlation in separable states-is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.

Can You Hear the Shape of a Drum?

If you had perfect pitch and listened to a recording of the sounds a drum made when struck, could you determine the shape of the drum? This question is an example of an inverse problem; inverse problems arise in medical imaging, oil prospecting, spectroscopy, and many other fields. We’ll first discuss the analogous question in the simpler setting of plucking a string. Then we’ll tackle the problem for drums and see that there are some surprises. Finally, I will give a brief indication of how this problem relates to some of my recent research. The emphasis will be on the ideas rather than on the technical details, so there will be pretty pictures instead of equations.