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pro vyhledávání: '"Lancien, Cecilia"'
Autor:
Lancien, Cécilia
In this work we investigate how quantum expanders (i.e. quantum channels with few Kraus operators but a large spectral gap) can be constructed from unitary designs. Concretely, we prove that a random quantum channel whose Kraus operators are independ
Externí odkaz:
http://arxiv.org/abs/2409.17971
We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Ot
Externí odkaz:
http://arxiv.org/abs/2404.19662
We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the limiting spectral
Externí odkaz:
http://arxiv.org/abs/2311.12368
Autor:
Lancien, Cécilia, Youssef, Pierre
We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In particular,
Externí odkaz:
http://arxiv.org/abs/2302.07772
Genuine multipartite entanglement of a given multipartite pure quantum state can be quantified through its geometric measure of entanglement, which, up to logarithms, is simply the maximum overlap of the corresponding unit tensor with product unit te
Externí odkaz:
http://arxiv.org/abs/2209.11754
Publikováno v:
Annales Henri Poincare, Vol. 25, No. 4 (2024) pp. 2107-2212
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better
Externí odkaz:
http://arxiv.org/abs/2206.10482
We introduce and study a class of entanglement criteria based on the idea of applying local contractions to an input multipartite state, and then computing the projective tensor norm of the output. More precisely, we apply to a mixed quantum state a
Externí odkaz:
http://arxiv.org/abs/2010.06365
Autor:
Lancien, Cécilia, Majenz, Christian
Publikováno v:
Quantum 4, 313 (2020)
Unitary $t$-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary $t$-designs. Building on results by Aubrun (Comm. Math. Phys
Externí odkaz:
http://arxiv.org/abs/1911.06742
Autor:
Lancien, Cécilia, Pérez-García, David
Publikováno v:
Ann. Henri Poincare (2021)
Tensor network states are used extensively as a mathematically convenient description of physically relevant states of many-body quantum systems. Those built on regular lattices, i.e. matrix product states (MPS) in dimension 1 and projected entangled
Externí odkaz:
http://arxiv.org/abs/1906.11682
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