We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an F-q-linear (n, q(hk), n - k + 1)(qh) MDS code over F-qh. If k = 3, h is an el...
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We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an F-q-linear (n, q(hk), n - k + 1)(qh) MDS code over F-qh. If k = 3, h is an element of {2, 3}, n > max {q(h-1), hq - 1} + 3, and C has three coordinates from which its projections are equivalent to Fqh-linear codes, we prove that C itself is equivalent to an F-qh-linear code. If k > 3, n > q + k, and there are two disjoint subsets of coordinates whose combined size is at most k - 2 from which the projections of C are equivalent to F-qh-linear codes, we prove that C is equivalent to a code which is linear over a larger field than F-q. (C) 2023 Elsevier Inc. All rights reserved.
We study a continuous-variable dense coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifes...
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We study a continuous-variable dense coding protocol, originally proposed to employ a two-mode squeezed state, using a general two-mode Gaussian state as a quantum channel. We particularly obtain conditions to manifest quantum advantage by beating two well-known single-mode schemes, namely, the squeezed-state scheme (best Gaussian scheme) and the number-state scheme (optimal scheme achieving the Holevo bound). We then extend our study to a multipartite Gaussian state and investigate the monogamy of operational entanglement measured by the communication capacity under the dense coding protocol. We show that this operational entanglement represents a strict monogamy relation, by means of Heisenberg's uncertainty principle among different parties; i.e., the quantum advantage for communication can be possible for only one pair of two-mode systems among many parties.
In this paper, we consider two related problems, unambiguous discrimination of quantum mixed states and unambiguously conveying classical messages using Einstein-Podolsky-Rosen (EPR) pairs. The main technical contribu...
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In this paper, we consider two related problems, unambiguous discrimination of quantum mixed states and unambiguously conveying classical messages using Einstein-Podolsky-Rosen (EPR) pairs. The main technical contributions are as follows. First, we present a general upper bound on the success probability for unambiguous discrimination among arbitrary N mixed quantum states with given a priori probability, which can be directly used to the unambiguous communication setting. Second, we propose a sufficient condition to show that a new upper bound can be achievable, and construct examples to clarify the relationship between the upper bound we derive and the existing upper bounds presented by other authors. Third, in the issue of conveying classical messages using EPR pairs, we also derive an upper bound on the success probability for unambiguously decoding, where Alice wants to convey n bit classical information to Bob by sending m quantum bits.
Let p be an odd prime and consider the finite field F-p2. Given a linear code C subset of F-p(2)n, we use algebraic number theory to construct an associated lattice Lambda(C) subset of O-L(n) for L an algebraic number...
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Let p be an odd prime and consider the finite field F-p2. Given a linear code C subset of F-p(2)n, we use algebraic number theory to construct an associated lattice Lambda(C) subset of O-L(n) for L an algebraic number field and O-L the ring of integers of L. We attach a theta series theta(Lambda C) to the lattice Lambda(C) and prove a relation between theta(Lambda C) and the complete weight enumerator evaluated on weight one theta series. (C) 2020 Elsevier Inc. All rights reserved.
Compressed sensing is a signal processing technique used to efficiently acquire and reconstruct signals across various fields, including science, engineering, and business. A critical research challenge in compressed ...
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Compressed sensing is a signal processing technique used to efficiently acquire and reconstruct signals across various fields, including science, engineering, and business. A critical research challenge in compressed sensing is constructing a sensing matrix with desirable reconstruction properties. For optimal performance, the reconstruction process requires the sensing matrix to have low coherence. Several methods have been proposed to create deterministic sensing matrices. We propose a new statistical method to construct deterministic sensing matrices by intelligently sampling rows of Walsh-Hadamard matrices. Compared to existing methods, our approach yields sensing matrices with lower coherence, accommodates a more flexible number of measurements, and entails lower computational cost.
Three different encoding mechanisms are combined to improve further steganographic embedding efficiency. They are secret-bit representation derived from the parity check coding, exploitation of the modification direct...
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Three different encoding mechanisms are combined to improve further steganographic embedding efficiency. They are secret-bit representation derived from the parity check coding, exploitation of the modification direction on pixel-values, and wet paper coding. The parity of least significant bit weight in each pixel-group is used to accommodate one secret bit. The weighted-sums of all pixel-groups and wet paper coding arc used to select which pixels arc modified and decide the way of modification as to whether to add or subtract one for carrying more secret data. It is shown that, by taking full advantage of these mechanisms, the embedding efficiency of the proposed scheme is higher than any of the previous steganographic embedding techniques.
作者：
C. CastelnovoTCM Group
Cavendish Laboratory University of Cambridge Cambridge CB3 0HE United Kingdom
In this paper we study the behavior of the entanglement measure dubbed negativity in the context of the toric code model. Using a replica method introduced recently by Calabrese, Cardy, and Tonni [Phys. Rev. Lett. 109...
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In this paper we study the behavior of the entanglement measure dubbed negativity in the context of the toric code model. Using a replica method introduced recently by Calabrese, Cardy, and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we obtain an exact expression which illustrates how the nonlocal correlations present in a topologically ordered state reflect in the behavior of the negativity of the system. We find that the negativity has a leading area-law contribution if the subsystems are in direct contact with one another (as expected in a zero-range correlated model). We also find a topological contribution directly related to the topological entropy, provided that the partitions are topologically nontrivial in both directions on a torus. We further confirm by explicit calculation that the negativity captures only quantum contributions to the entanglement. Indeed, we show that the negativity vanishes identically for the classical topologically ordered eight-vertex model, which on the contrary exhibits a finite von Neumann entropy, inclusive of topological correction.
Distances for taking evacuation as a protective measure during early phase of a nuclear accident have been approximated using MELCOR Accident Consequence Code System (MACCS). As a reference data, the source term of Pa...
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Distances for taking evacuation as a protective measure during early phase of a nuclear accident have been approximated using MELCOR Accident Consequence Code System (MACCS). As a reference data, the source term of Pakistan Research Reactor 1 (PARR-1) and meteorological data of Islamabad, Pakistan, have been considered. Based on comparison with published data and international radiological assessment (InterRAS) code results, it is concluded that MACCS is a rational tool for estimation of urgent protective actions during early phase of nuclear accident by taking into account the variations in meteorological and release concentrations parameters.
Optimal penal codes are constructed for a class of infinitely repeated games with discounting. These games can be interpreted as Bertrand oligopoly games with capacity constraints. No particular rationing rule is adop...
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Optimal penal codes are constructed for a class of infinitely repeated games with discounting. These games can be interpreted as Bertrand oligopoly games with capacity constraints. No particular rationing rule is adopted; weak restrictions are imposed on the firms' sales functions instead. Models adopting the commonly used rationing rules are special cases of the general framework studied here. It is found that firms can be driven to their security levels by credible punishments.
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