Goren Gordon

Generalized quantum-state sharing

We present two quantum-state sharing protocols where the channels are not maximally entangled states. By properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state if the parties collaborate. We also show that contrary to the protocols where we have maximally entangled channels these protocols are probabilistic. We then compare the efficiency of both protocols and sketch the generalization of the protocols to N parties.

Generalized teleportation protocol

A generalized teleportation protocol (GTP) for N qubits is presented, where the teleportation channels are nonmaximally entangled and all the free parameters of the protocol are considered: Alices measurement basis, her sets of acceptable results, and Bobs unitary operations. The full range of fidelity (F) of the teleported state and the probability of success (P{sub suc}) to obtain a given fidelity are achieved by changing these free parameters. A channel efficiency bound is found, where one can determine how to divide it between F and P{sub suc}. A one-qubit formulation is presented and then expanded to N qubits. A proposed experimental setup that implements the GTP is given using linear optics.

Thermodynamic control by frequent quantum measurements

Heat flow between a large thermal ‘bath’ and a smaller system brings them progressively closer to thermal equilibrium while increasing their entropy. Fluctuations involving a small fraction of a statistical ensemble of systems interacting with the bath result in deviations from this trend. In this respect, quantum and classical thermodynamics are in agreement. Here we predict a different trend in a purely quantum mechanical setting: disturbances of thermal equilibrium between two-level systems (TLSs) and a bath, caused by frequent, brief quantum non-demolition measurements of the TLS energy states. By making the measurements increasingly frequent, we encounter first the anti-Zeno regime and then the Zeno regime (namely where the TLSs’ relaxation respectively speeds up and slows down). The corresponding entropy and temperature of both the system and the bath are then found to either decrease or increase depending only on the rate of observation, contrary to the standard thermodynamical rules that hold for memory-less (Markov) baths. From a practical viewpoint, these anomalies may offer the possibility of very fast control of heat and entropy in quantum systems, allowing cooling and state purification over an interval much shorter than the time needed for thermal equilibration or for a feedback control loop.

Optimal dynamical decoherence control of a qubit.

We present a theory of dynamical control by modulation for optimal decoherence reduction. The theory is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.

Motor-Sensory Confluence in Tactile Perception

Perception involves motor control of sensory organs. However, the dynamics underlying emergence of perception from motor-sensory interactions are not yet known. Two extreme possibilities are as follows: (1) motor and sensory signals interact within an open-loop scheme in which motor signals determine sensory sampling but are not affected by sensory processing and (2) motor and sensory signals are affected by each other within a closed-loop scheme. We studied the scheme of motor-sensory interactions in humans using a novel object localization task that enabled monitoring the relevant overt motor and sensory variables. We found that motor variables were dynamically controlled within each perceptual trial, such that they gradually converged to steady values. Training on this task resulted in improvement in perceptual acuity, which was achieved solely by changes in motor variables, without any change in the acuity of sensory readout. The within-trial dynamics is captured by a hierarchical closed-loop model in which lower loops actively maintain constant sensory coding, and higher loops maintain constant sensory update flow. These findings demonstrate interchangeability of motor and sensory variables in perception, motor convergence during perception, and a consistent hierarchical closed-loop perceptual model.

Preventing multipartite disentanglement by local modulations.

An entangled multipartite system coupled to a zero-temperature bath undergoes rapid disentanglement in many realistic scenarios due to local, symmetry-breaking differences in the particle-bath couplings. We show that locally controlled perturbations, addressing each particle individually, can impose a symmetry allowing the existence of decoherence-free multipartite entangled systems.

Universal dynamical decoherence control of noisy single- and multi-qubit systems

In this paper, we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude or phase noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.

2012 Special Issue: Hierarchical curiosity loops and active sensing

A curious agent acts so as to optimize its learning about itself and its environment, without external supervision. We present a model of hierarchical curiosity loops for such an autonomous active learning agent, whereby each loop selects the optimal action that maximizes the agents learning of sensory-motor correlations. The model is based on rewarding the learners prediction errors in an actor-critic reinforcement learning (RL) paradigm. Hierarchy is achieved by utilizing previously learned motor-sensory mapping, which enables the learning of other mappings, thus increasing the extent and diversity of knowledge and skills. We demonstrate the relevance of this architecture to active sensing using the well-studied vibrissae (whiskers) system, where rodents acquire sensory information by virtue of repeated whisker movements. We show that hierarchical curiosity loops starting from optimally learning the internal models of whisker motion and then extending to object localization result in free-air whisking and object palpation, respectively.

Direct measurement of the system–environment coupling as a tool for understanding decoherence and dynamical decoupling

Decoherence is a major obstacle to any practical implementation of quantum information processing. One of the leading strategies to reduce decoherence is dynamical decoupling—the use of an external field to average out the effect of the environment. The decoherence rate under any control field can be calculated if the spectrum of the coupling to the environment is known. We present a direct measurement of the bath-coupling spectrum in an ensemble of optically trapped ultra-cold atoms, by applying a spectrally narrow-band control field. The measured spectrum follows a Lorentzian shape at low frequencies but exhibits non-monotonic features at higher frequencies due to the oscillatory motion of the atoms in the trap. These features agree with our analytical models and numerical Monte Carlo simulations of the collisional bath. From the inferred bath-coupling spectrum, we predict the performance of some well-known dynamical decoupling sequences. We then apply these sequences in experiment and compare the results to predictions, finding good agreement in the weak-coupling limit. Thus, our work establishes experimentally the validity of the overlap integral formalism and is an important step towards the implementation of an optimal dynamical decoupling sequence for a given measured bath spectrum.

Toward an Integrated Approach to Perception and Action: Conference Report and Future Directions

This article was motivated by the conference entitled “Perception & Action – An Interdisciplinary Approach to Cognitive Systems Theory,” which took place September 14–16, 2010 at the Santa Fe Institute, NM, USA. The goal of the conference was to bring together an interdisciplinary group of neuroscientists, roboticists, and theorists to discuss the extent and implications of action–perception integration in the brain. The motivation for the conference was the realization that it is a widespread approach in biological, theoretical, and computational neuroscience to investigate sensory and motor function of the brain in isolation from one another, while at the same time, it is generally appreciated that sensory and motor processing cannot be fully separated. Our article summarizes the key findings of the conference, provides a hypothetical model that integrates the major themes and concepts presented at the conference, and concludes with a perspective on future challenges in the field.