Entangled qubits can increase the capacity of quantum error-correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do ...
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Entangled qubits can increase the capacity of quantum error-correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and nonadditive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common stabilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only on the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors in the codeword stabilized quantum code framework give rise to effective Z errors on Bob's side. We use this scheme to construct entanglement-assisted nonadditive quantum codes, in particular, ((5,16,2;1)) and ((7,4,5;4)) codes.
We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a grap...
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We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or nonadditive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.
In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over GF(q), the Galois Field of order q. We present a scheme of low complexity and near-optimal empir...
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In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over GF(q), the Galois Field of order q. We present a scheme of low complexity and near-optimal empirical performance. The compression step is based on a reduction of a sparse low-density parity-check code over GF(q) and is done through the so-called reinforced belief-propagation equations. These reduced codes appear to have a nontrivial geometrical modification of the space of codewords, which makes such compression computationally feasible. The computational complexity is O(dnqlog2q) per iteration, where d is the average degree of the check nodes and n is the number of bits. For our code ensemble, decompression can be done in a time linear in the code's length by a simple leaf-removal algorithm.
We propose an alternate measure of information, called superinformation, which has been found to be very effective for analyzing the coding and noncoding regions of the DNA. This superinformation is actually a measure...
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We propose an alternate measure of information, called superinformation, which has been found to be very effective for analyzing the coding and noncoding regions of the DNA. This superinformation is actually a measure of the “randomness of randomness.” It has been found to be highly accurate in classifying coding and noncoding regions of human DNA. In the proposed method, no prior training is required. This technique exhibits higher accuracy than previously reported techniques in distinguishing between the coding and the noncoding portions of the DNA. Superinformation can also be used to analyze the untranslated regions in various genes.
Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are cons...
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Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimensions.
A description of how the activity of a population of neurons reflects the structure of its inputs is essential for understanding neural coding. Many studies have examined how inputs determine spiking statistics, while...
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A description of how the activity of a population of neurons reflects the structure of its inputs is essential for understanding neural coding. Many studies have examined how inputs determine spiking statistics, while comparatively little is known about membrane potentials. We examine how membrane potential statistics are related to input and spiking statistics. Surprisingly, firing rates and membrane potentials are sensitive to input current modulations in distinct regimes. Additionally, the correlation between the membrane potentials of two uncoupled cells and the correlation between their spike trains reflect input correlations in distinct regimes. Our predictions are experimentally testable, provide insight into the filtering properties of neurons, and indicate that care needs to be taken when interpreting neuronal recordings that reflect a combination of subthreshold and spiking activity.
Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containi...
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Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.
The paper devoted to implementation of the public key algorithm based on directed algebraic graphs over finite commutative ring K and their symmetries. First we expand the key space K n of graph based encryption algor...
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The paper devoted to implementation of the public key algorithm based on directed algebraic graphs over finite commutative ring K and their symmetries. First we expand the key space K n of graph based encryption algorithm in such way that arbitrary chosen plaintext can be converted to arbitrary chosen ciphertext. Second, we conjugate chosen encryption map, which is a composition of several “elementary” cubical polynomial automorphisms of a free module K n with special invertible affine transformation of K n . Finally we compute symbolically corresponding cubic public map g of K n onto K n . We evaluate time for the generation of g , time of execution of public map, number of monomial expression in the list of corresponding public rules.
Subjective testing is the most direct means of assessing multimedia quality as experienced by users. When multiple dimensions must be evaluated, these tests can become slow and costly. We present gradient ascent subje...
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Subjective testing is the most direct means of assessing multimedia quality as experienced by users. When multiple dimensions must be evaluated, these tests can become slow and costly. We present gradient ascent subjective testing (GAST) as an efficient way to locate optimizing sets of coding or transmission parameter values. GAST combines gradient ascent optimization techniques with subjective test trials. As a proof-of-concept, we used GAST to search a two-dimensional parameter space for the known region of maximal audio quality, using paired-comparison listening trials. That region was located accurately and much more efficiently than use of an exhaustive search. We also used GAST to search a two-dimensional quantizer design space for a point of maximal image quality, using side-by-side paired-comparison trials. The point of maximal image quality was efficiently located, and the corresponding quantizer shape and deadzone agree closely with the quantizer specifications for JPEG 2000, Part 1.
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