윤상균 교수

The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory (QIT). It was solved by Matthew B. Hastings [“Superadditivity of communication capacity using entangled inputs”, Nature Physics 5, 255–257 (2009; doi:)] in the one-shot case by exhibiting a pair of random quantum channels. However, the initial motivation was arguably to understand regularized quantities, and there was so far no way to solve additivity questions in the regularized ca

Abstract One of the fundamental questions in quantum information theory is determining entanglement of quantum states, which is generally an NP-hard problem. In this paper, we prove that all PPT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mover> <mml:mi>π</mml:mi> <mml:mo accent="true">―</mml:mo> </mml:mover> <mml:mi>A</mml:mi> </mml:msub> <mml:mo>⊗</mml:mo> <mml:msub> <mml:mi>π</mml:mi> <mml:mi>B</mml

We investigate information theoretic properties of low rank (less than or equal to 3) quantum channels with [Formula: see text]-symmetry, where we have a complete description. We prove that PPT property coincides with entanglement-breaking property and that degradability seldomly holds in this class. In connection with these results, we will demonstrate how we can compute Holevo and coherent information of those channels. In particular, we exhibit a strong form of additivity violation of coheren

Abstract In this paper, we present a new application of group theory to develop a systematical approach to efficiently compute the Schmidt numbers. The Schmidt number is a natural quantification of entanglement in quantum information theory, but computing its exact value is generally a challenging task even for very concrete examples. We exhibit a complete characterization of all orthogonally covariant k -positive maps. This result generalizes earlier results by Tomiyama (Linear Algebra Appl 69:

The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory. It was solved by Hastings in 2009 in the one-shot case, by exhibiting a pair of super-additive channels. The purpose of this paper is to give a solution to the problem in the regularized case. Specifically, we exhibit a quantum channel for which the regularized minimum output entropy is super-additive. Unlike previously known results in the one-shot case, our construction is non-ra

The uncertainty principle has been established within the framework of locally compact quantum groups in recent years. This paper demonstrates that entropic uncertainty relations can be strengthened under localizations on discrete quantum groups, which is the case if the dual compact quantum group G is the free orthogonal quantum group ON+ with N ≥ 3 or if G admits an infinite Λ(p) set with p &amp;gt; 2. On the other hand, this paper explains the reason why such phenomena do not appear when G is

Abstract We develop a theory of Gaussian states over general quantum kinematical systems with finitely many degrees of freedom. The underlying phase space is described by a locally compact abelian (LCA) group G with a symplectic structure determined by a 2-cocycle on G . We use the concept of Gaussian distributions on LCA groups in the sense of Bernstein to define Gaussian states and completely characterize Gaussian states over 2-regular LCA groups of the form $$G= F\times \widehat{F}$$ <mml:mat

In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information about the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we inve

Helgason showed that a given measure $f\in M(G)$ on a compact group $G$ should be in $L^2(G)$ automatically if all random Fourier series of $f$ are in $M(G)$. We explore a natural analogue of the theorem in the framework of compact quantum groups and apply the obtained results to study complete representability problem for convolution algebras of compact quantum groups as an operator algebra.

We present natural analogues of strong Haagerup inequalities on non-Kac free orthogonal quantum groups $O_F^+$ in which $L^p$-analytic problems are harder due to their non-tracial nature. Furthermore, we prove optimality of the inequalities, and apply the obtained results to compute the optimal time for ultracontractivity of the heat semigroup and to distinguish the complex interpolation space $L^p(O_F^+)$ and the real interpolation space $L^{p,p}(O_F^+)$.

We study the optimal order of natural analogues of Sobolev embedding properties within the framework of compact matrix quantum groups of Kac type. One of the main results of this paper is that the optimal order is given by the polynomial growth order of dual discrete quantum groups in a broad class, which covers all connected compact Lie groups, duals of polynomially growing discrete groups, $ O_2^+ $ and $ S_4^+ $. Outside the realm of co-amenable compact quantum groups, we prove that the optim

Abstract The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [10] established asymptotic freeness between partial transposes in the bipartite situation. In this paper, we prove almost sure asymptotic freeness in the general multipartite situation and establish a central limit theorem for the partial transposes.

We establish sharp Sobolev embedding properties within a broad class of\ncompact matrix quantum groups of Kac type under the polynomial growth or the\nrapid decay property of their duals. Main examples are duals of polynomially\ngrowing discrete quantum groups, duals of free groups and free quantum groups\n$O_N^+,S_N^+$. In addition, we generalize sharpend Hausdorff-Young\ninequalities, compute degrees of the rapid decay property for\n$\\widehat{O_N^+},\\widehat{S_N^+}$ and prove sharpness of Ha