Robust cue integration: a Bayesian model and evidence from cueconflict studies with stereoscopic and figure cues to slant.

Most research on depth cue integration has focused on stimulus regimes in which stimuli contain the small cue conflicts that one might expect to normally arise from sensory noise. In these regimes, linear models for cue integration provide a good approximation to system performance. This article focuses on situations in which large cue conflicts can naturally occur in stimuli. We describe a Bayesian model for nonlinear cue integration that makes rational inferences about scenes across the entire range of possible cue conflicts. The model derives from the simple intuition that multiple properties of scenes or causal factors give rise to the image information associated with most cues. To make perceptual inferences about one property of a scene, an ideal observer must necessarily take into account the possible contribution of these other factors to the information provided by a cue. In the context of classical depth cues, large cue conflicts most commonly arise when one or another cue is generated by an object or scene that violates the strongest form of constraint that makes the cue informative. For example, when binocularly viewing a slanted trapezoid, the slant interpretation of the figure derived by assuming that the figure is rectangular may conflict greatly with the slant suggested by stereoscopic disparities. An optimal Bayesian estimator incorporates the possibility that different constraints might apply to objects in the world and robustly integrates cues with large conflicts by effectively switching between different internal models of the prior constraints underlying one or both cues. We performed two experiments to test the predictions of the model when applied to estimating surface slant from binocular disparities and the compression cue (the aspect ratio of figures in an image). The apparent weight that subjects gave to the compression cue decreased smoothly as a function of the conflict between the cues but did not shrink to zero; that is, subjects did not fully veto the compression cue at large cue conflicts. A Bayesian model that assumes a mixed prior distribution of figure shapes in the world, with a large proportion being very regular and a smaller proportion having random shapes, provides a good quantitative fit for subjects' performance. The best fitting model parameters are consistent with the sensory noise to be expected in measurements of figure shape, further supporting the Bayesian model as an account of robust cue integration

Optimal and Efficient Decoding of Concatenated Quantum Block Codes

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However, we demonstrate that for concatenated block codes, the optimal decoding can be efficiently computed using a message passing algorithm. We compare the performance of the message passing algorithm to that of the widespread blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message passing algorithms in two respects. 1) Optimal decoding increases by as much as 94% the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel. 2) For noise levels below these thresholds, the probability of error after optimal decoding is suppressed at a significantly higher rate, leading to a substantial reduction of the error correction overhead.Comment: Published versio

Hiding bits in Bell states

We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in $n$, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.Comment: 4 pages RevTex, 1 figure, various small changes and additional paragraph on optics implementatio

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of the system under study. This is a square root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.Comment: Minor changes taking into account Howard Wiseman's comment: quant-ph/0305153. Accepted for publication in Phys. Rev.

Quantum Channel Capacity of Very Noisy Channels

We present a family of additive quantum error-correcting codes whose capacities exceeds that of quantum random coding (hashing) for very noisy channels. These codes provide non-zero capacity in a depolarizing channel for fidelity parameters $f$ when $f> .80944$. Random coding has non-zero capacity only for $f>.81071$; by analogy to the classical Shannon coding limit, this value had previously been conjectured to be a lower bound. We use the method introduced by Shor and Smolin of concatenating a non-random (cat) code within a random code to obtain good codes. The cat code with block size five is shown to be optimal for single concatenation. The best known multiple-concatenated code we found has a block size of 25. We derive a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states.Comment: 31 pages including epsf postscript figures. Replaced to correct important typographical errors in equations 36, 37 and in tex

Toy Model for a Relational Formulation of Quantum Theory

In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.Comment: References added, extended discussio