Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs

We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled stabilizer states as MUB vectors. Consequently, these bipartite entangled stabilizer MUBs (BES MUBs) provide no local information, but are sufficient and minimal for decomposing a wide variety of interesting operators including (mixtures of) Jamiolkowski states, entanglement witnesses and more. The problem of finding such BES MUBs can be mapped, in a natural way, to that of finding maximum cliques in a family of Cayley graphs. Some relationships with known power-of-prime MUB constructions are discussed, and observables for BES MUBs are given explicitly in terms of Pauli operators.Comment: 8 pages, 1 figur

The SIC Question: History and State of Play

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.Comment: 16 pages, 1 figure, many references; v3: updating bibliography, dimension eight hundred forty fou

Hybrid LSTM and Encoder-Decoder Architecture for Detection of Image Forgeries

With advanced image journaling tools, one can easily alter the semantic meaning of an image by exploiting certain manipulation techniques such as copy-clone, object splicing, and removal, which mislead the viewers. In contrast, the identification of these manipulations becomes a very challenging task as manipulated regions are not visually apparent. This paper proposes a high-confidence manipulation localization architecture which utilizes resampling features, Long-Short Term Memory (LSTM) cells, and encoder-decoder network to segment out manipulated regions from non-manipulated ones. Resampling features are used to capture artifacts like JPEG quality loss, upsampling, downsampling, rotation, and shearing. The proposed network exploits larger receptive fields (spatial maps) and frequency domain correlation to analyze the discriminative characteristics between manipulated and non-manipulated regions by incorporating encoder and LSTM network. Finally, decoder network learns the mapping from low-resolution feature maps to pixel-wise predictions for image tamper localization. With predicted mask provided by final layer (softmax) of the proposed architecture, end-to-end training is performed to learn the network parameters through back-propagation using ground-truth masks. Furthermore, a large image splicing dataset is introduced to guide the training process. The proposed method is capable of localizing image manipulations at pixel level with high precision, which is demonstrated through rigorous experimentation on three diverse datasets

Minimal average degree aberration and the state polytope for experimental designs

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic method does not in general produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on "aberration" and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase