Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic

We describe generalizations of the Pauli group, the Clifford group and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over the integers modulo d. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.Comment: 10 pages, RevTe

Stabilizer state breeding

We present a breeding protocol that distills pure copies of any stabilizer state from noisy copies and a pool of predistilled pure copies of the same state, by means of local Clifford operations, Pauli measurements and classical communication.Comment: RevTeX4, 9 pages, 1 figur

The role of right and left parietal lobes in the conceptual processing of numbers

Neuropsychological and functional imaging studies have associated the conceptual processing of numbers with bilateral parietal regions (including intraparietal sulcus). However, the processes driving these effects remain unclear because both left and right posterior parietal regions are activated by many other conceptual, perceptual, attention, and response-selection processes. To dissociate parietal activation that is number-selective from parietal activation related to other stimulus or response-selection processes, we used fMRI to compare numbers and object names during exactly the same conceptual and perceptual tasks while factoring out activations correlating with response times. We found that right parietal activation was higher for conceptual decisions on numbers relative to the same tasks on object names, even when response time effects were fully factored out. In contrast, left parietal activation for numbers was equally involved in conceptual processing of object names. We suggest that left parietal activation for numbers reflects a range of processes, including the retrieval of learnt facts that are also involved in conceptual decisions on object names. In contrast, number selectivity in right parietal cortex reflects processes that are more involved in conceptual decisions on numbers than object names. Our results generate a new set of hypotheses that have implications for the design of future behavioral and functional imaging studies of patients with left and right parietal damage

An Accumulator Model for Spontaneous Neural Activity Prior to Self-Initiated Movement

A gradual buildup of neuronal activity known as the “readiness potential” reliably precedes voluntary self-initiated movements, in the average timelocked tomovement onset. This buildup is presumed to reflect the final stages of planning and preparation for movement. Here we present a different interpretation of the premovement buildup.We used a leaky stochastic accumulator tomodel the neural decision of “when” to move in a task where there is no specific temporal cue, but only a general imperative to produce amovement after an unspecified delay on the order of several seconds. According to our model, when the imperative to produce a movement is weak, the precise moment at which the decision threshold is crossed leading tomovement is largely determined by spontaneous subthreshold fluctuations in neuronal activity. Time locking to movement onset ensures that these fluctuations appear in the average as a gradual exponential-looking increase in neuronal activity. Our model accounts for the behavioral and electroencephalography data recorded from human subjects performing the task and also makes a specific prediction that we confirmed in a second electroencephalography experiment: Fast responses to temporally unpredictable interruptions should be preceded by a slow negative-going voltage deflection beginning well before the interruption itself, even when the subject was not preparing to move at that particular moment

Improvement of stabilizer based entanglement distillation protocols by encoding operators

This paper presents a method for enumerating all encoding operators in the Clifford group for a given stabilizer. Furthermore, we classify encoding operators into the equivalence classes such that EDPs (Entanglement Distillation Protocol) constructed from encoding operators in the same equivalence class have the same performance. By this classification, for a given parameter, the number of candidates for good EDPs is significantly reduced. As a result, we find the best EDP among EDPs constructed from [[4,2]] stabilizer codes. This EDP has a better performance than previously known EDPs over wide range of fidelity.Comment: 22 pages, 2 figures, In version 2, we enumerate all encoding operators in the Clifford group, and fix the wrong classification of encoding operators in version

How to play two-players restricted quantum games with 10 cards

We show that it is perfectly possible to play 'restricted' two-players, two-strategies quantum games proposed originally by Marinatto and Weber having as the only equipment a pack of 10 cards. The 'quantum board' of such a model of these quantum games is an extreme simplification of 'macroscopic quantum machines' proposed by one of the authors in numerous papers that allow to simulate by macroscopic means various experiments performed on two entangled quantum objectsComment: 4 pages, 3 figure

Local permutations of products of Bell states and entanglement distillation

We present new algorithms for mixed-state multi-copy entanglement distillation for pairs of qubits. Our algorithms perform significantly better than the best known algorithms. Better algorithms can be derived that are tuned for specific initial states. The new algorithms are based on a characterization of the group of all locally realizable permutations of the 4^n possible tensor products of n Bell states.Comment: 6 pages, 1 figur

Monotonic Coding of Numerosity in Macaque Lateral Intraparietal Area

As any child knows, the first step in counting is summing up individual elements, yet the brain mechanisms responsible for this process remain obscure. Here we show, for the first time, that a population of neurons in the lateral intraparietal area of monkeys encodes the total number of elements within their classical receptive fields in a graded fashion, across a wide range of numerical values (2–32). Moreover, modulation of neuronal activity by visual quantity developed rapidly, within 100 ms of stimulus onset, and was independent of attention, reward expectations, or stimulus attributes such as size, density, or color. The responses of these neurons resemble the outputs of “accumulator neurons” postulated in computational models of number processing. Numerical accumulator neurons may provide inputs to neurons encoding specific cardinal values, such as “4,” that have been described in previous work. Our findings may explain the frequent association of visuospatial and numerical deficits following damage to parietal cortex in humans

Stabilizer notation for Spekkens' toy theory

Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in order to argue for an epistemic view of quantum states. I describe a notation for the theory (excluding certain joint measurements) which makes its similarities and differences with the quantum mechanics of stabilizer states clear. Given an application of the qubit stabilizer formalism, it is often entirely straightforward to construct an analogous application of the notation to the toy theory. This assists calculations within the toy theory, for example of the number of possible states and transformations, and enables superpositions to be defined for composite systems.Comment: 7+4 pages, 5 tables. v2: Clarifications added and typos fixed in response to referee comment

Hearing faces: how the infant brain matches the face it sees with the speech it hears

Speech is not a purely auditory signal. From around 2 months of age, infants are able to correctly match the vowel they hear with the appropriate articulating face. However, there is no behavioral evidence of integrated audiovisual perception until 4 months of age, at the earliest, when an illusory percept can be created by the fusion of the auditory stimulus and of the facial cues (McGurk effect). To understand how infants initially match the articulatory movements they see with the sounds they hear, we recorded high-density ERPs in response to auditory vowels that followed a congruent or incongruent silently articulating face in 10-week-old infants. In a first experiment, we determined that auditory–visual integration occurs during the early stages of perception as in adults. The mismatch response was similar in timing and in topography whether the preceding vowels were presented visually or aurally. In the second experiment, we studied audiovisual integration in the linguistic (vowel perception) and nonlinguistic (gender perception) domain. We observed a mismatch response for both types of change at similar latencies. Their topographies were significantly different demonstrating that cross-modal integration of these features is computed in parallel by two different networks. Indeed, brain source modeling revealed that phoneme and gender computations were lateralized toward the left and toward the right hemisphere, respectively, suggesting that each hemisphere possesses an early processing bias. We also observed repetition suppression in temporal regions and repetition enhancement in frontal regions. These results underscore how complex and structured is the human cortical organization which sustains communication from the first weeks of life on