Marius Junge
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View article: Strong converse rate for asymptotic hypothesis testing in type III
Strong converse rate for asymptotic hypothesis testing in type III Open
We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative Rényi entropy in the strong converse of h…
View article: Transportation cost and contraction coefficient for channels on von Neumann algebras
Transportation cost and contraction coefficient for channels on von Neumann algebras Open
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to m…
View article: Embeddings of symmetric operator spaces into Lp-spaces, 1 ≤ p < 2, on finite von Neumann algebras
Embeddings of symmetric operator spaces into Lp-spaces, 1 ≤ p < 2, on finite von Neumann algebras Open
Let E (0, ∞) be a symmetric function space on (0, ∞) such that the set E (0, ∞) ∩ L ∞ (0, ∞) is distinct from the set L p (0, ∞)∩ L ∞ (0, ∞), 1 ≤ p < 2, and let $$E(\cal M)$$ be the corresponding symmetric operator space associated wi…
View article: Complete positivity order and relative entropy decay
Complete positivity order and relative entropy decay Open
We prove that for a GNS-symmetric quantum Markov semigroup, the complete modified logarithmic Sobolev constant is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this gives a short proof that…
View article: Graph Hörmander Systems
Graph Hörmander Systems Open
This paper extends the Bakry-Émery criterion relating the Ricci curvature and logarithmic Sobolev inequalities to the noncommutative setting. We obtain easily computable complete modified logarithmic Sobolev inequalities of graph Laplacian…
View article: Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach
Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach Open
Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on establi…
View article: On a question of Blecher, Pisier, Shlyakhtenko
On a question of Blecher, Pisier, Shlyakhtenko Open
We show the failure of a matricial version of Grothendieck's theorem for operator spaces, thereby resolving a long-standing open question in the field. Moreover, by showing that such a counterexample can occur in the simplest context of co…
View article: Quantum secret sharing and tripartite information
Quantum secret sharing and tripartite information Open
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application …
View article: Noncommutative Poisson Random Measure and Its Applications
Noncommutative Poisson Random Measure and Its Applications Open
We introduce a noncommutative Poisson random measure on a von Neumann algebra. This is a noncommutative generalization of the classical Poisson random measure. We call this construction Poissonization. Poissonization is a functor from the …
View article: Resource-Dependent Complexity of Quantum Channels
Resource-Dependent Complexity of Quantum Channels Open
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By l…
View article: On the power of quantum entanglement in multipartite quantum XOR games
On the power of quantum entanglement in multipartite quantum XOR games Open
In this paper we show that, given $k\geq 3$, there exist $k$-player quantum XOR games for which the entangled bias can be arbitrarily larger than the bias of the game when the players are restricted to separable strategies. In particular, …
View article: Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels
Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels Open
We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's alg…
View article: Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings
Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings Open
Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, moti…
View article: Stability property for the quantum jump operators of an open system
Stability property for the quantum jump operators of an open system Open
We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space …
View article: The Communication Value of a Quantum Channel
The Communication Value of a Quantum Channel Open
There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected clas…
View article: Entropy Decay Estimates For Collective Noise Models
Entropy Decay Estimates For Collective Noise Models Open
One of the challenges in quantum information science is to control open quantum systems with a large number of qubits. An important aspect of many-body systems is the emergence of collective phenomena. One collective noise model is an open…
View article: Relative entropy decay and complete positivity mixing time
Relative entropy decay and complete positivity mixing time Open
We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given b…
View article: On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games
On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games Open
In this work we show that, given a linear map from a general operator space into the dual of a C⁎-algebra, its completely bounded norm is upper bounded by a universal constant times its (1,cb)-summing norm. This problem is motivated by the…
View article: Quantum Euclidean spaces with noncommutative derivatives
Quantum Euclidean spaces with noncommutative derivatives Open
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical c…
View article: On the relation between completely bounded and $(1,cb)$-summing maps with applications to quantum XOR games
On the relation between completely bounded and $(1,cb)$-summing maps with applications to quantum XOR games Open
In this work we show that, given a linear map from a general operator space into the dual of a C$^*$-algebra, its completely bounded norm is upper bounded by a universal constant times its $(1,cb)$-summing norm. This problem is motivated b…
View article: Approximately low-rank recovery from noisy and local measurements by convex program
Approximately low-rank recovery from noisy and local measurements by convex program Open
Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrog…
View article: The Communication Value of a Quantum Channel
The Communication Value of a Quantum Channel Open
There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected clas…
View article: Notes on real interpolation of operator $L_p$-spaces
Notes on real interpolation of operator $L_p$-spaces Open
Let $\mathcal{M}$ be a semifinite von Neumann algebra. We equip the associated noncommutative $L_p$-spaces with their natural operator space structure introduced by Pisier via complex interpolation. On the other hand, for $1
View article: Singular integrals in quantum Euclidean spaces
Singular integrals in quantum Euclidean spaces Open
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential c…
View article: Geometric Approach Towards Complete Logarithmic Sobolev Inequalities
Geometric Approach Towards Complete Logarithmic Sobolev Inequalities Open
In this paper, we use the Carnot-Caratheodory distance from sub-Riemanian geometry to prove entropy decay estimates for all finite dimensional symmetric quantum Markov semigroups. This estimate is independent of the environment size and he…
View article: Relative Embeddability of von Neumann Algebras and Amalgamated Free Products
Relative Embeddability of von Neumann Algebras and Amalgamated Free Products Open
In this paper we study conditions under which, for an inclusion of finite von Neumann algebras $N \subseteq M$, we have the reduced amalgamated free product $\ast_N M$ is embeddable into $(R \bar{\otimes} N_1)^ω$ for some other finite von …