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Symmetry protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension (1D). Here, we formulate this phenomenon in the framework of symmetry-resolved entanglement (SRE) using cohomology…
Focusing on the particular case of the discrete symmetry group Z_N x Z_N, we establish a mapping between symmetry protected topological phases and symmetry broken phases for one-dimensional spin systems. It is realized in terms of a…
Consider recovering a rank-one tensor of size $n_1 \times \cdots \times n_d$ from exact or noisy observations of a few of its entries. We tackle this problem via semidefinite programming (SDP). We derive deterministic combinatorial…
The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of…
We propose a simple universal (that is, distribution--free) steganographic system in which covertexts with and without hidden texts are statistically indistinguishable. The stegosystem can be applied to any source generating i.i.d.…
Integer data is typically made differentially private by adding noise from a Discrete Laplace (or Discrete Gaussian) distribution. We study the setting where differential privacy of a counting query is achieved using bit-wise randomized…
Current security techniques can be implemented with either secret key exchange or physical layer wiretap codes. In this work, we investigate an alternative solution for MIMO wiretap channels. Inspired by the artificial noise (AN) technique,…
This paper revisits formalizations of information-theoretic security for symmetric-key encryption and key agreement protocols which are very fundamental primitives in cryptography. In general, we can formalize information-theoretic security…
Shallow quantum circuits feature not only computational advantages over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical…
We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional…
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for p and q prime. We first present a classification of these groups in five classes. Then, we…
Consequences of Schr\"{o}dinger's antipodal identification on quantum field theory in de Sitter space are investigated. The elliptic $\mathbb{Z}_2$ identification provides observers with complete information. We show that a suitable…
The $\hybrid$ model was recently introduced by Augustine et al. \cite{DBLP:conf/soda/AugustineHKSS20} in order to characterize from an algorithmic standpoint the capabilities of networks which combine multiple communication modes.…
We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements…
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots…
We demonstrate that the coherence of a single mobile atomic qubit can be well preserved during a transfer process among different optical dipole traps (ODTs). This is a prerequisite step in realizing a large-scale neutral atom quantum…
We develop a theory of asymptotic efficiency in regular parametric models when data confidentiality is ensured by local differential privacy (LDP). Even though efficient parameter estimation is a classical and well-studied problem in…