Completely Bounded Qusi-Norms, Their Mutiplicativity, and New Additivity Results of Quantum Channels

• URL: http://arxiv.org/abs/2603.16722v1
• Date: Tue, 17 Mar 2026 16:09:22 GMT
• Title: Completely Bounded Qusi-Norms, Their Mutiplicativity, and New Additivity Results of Quantum Channels
• Abstract summary: We obtain two new additivity results of quantum channels.<n>The first is the additivity of the channel Rényi information associated with the sandwiched Rényi divergence of order $in[frac12,1)$.<n>The second is the additivity of the channel dispersion, which is a quantity related to the second-order behavior of quantum information tasks.
• Score: 5.471107107177669
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We obtain two new additivity results of quantum channels. The first one is the additivity of the channel Rényi information associated with the sandwiched Rényi divergence of order $α\in[\frac{1}{2},1)$. To prove this, we introduce the completely bounded $1\toα$ quasi-norms for completely positive maps, with $α\in[\frac{1}{2},1)$, and show that it is multiplicative. The additivity/multiplicativity derived here extends and complements the results of Devetak {\it et al} (Commun Math Phys 266:37-63, 2006) and Gupta and Wilde (Commun Math Phys 334:867-887, 2015), which deal with the case $α>1$. The second one is the additivity of the channel dispersion, which is a quantity related to the second-order behavior of quantum information tasks.

Related papers

• Rényi Entanglement of Purification Is Non-additive [3.151184728006369]
  Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved.<n>We study its additivity for classical states on two qubits at different Rényi orders.
  arXiv  Detail & Related papers  (2026-08-28T21:54:33Z)
• Additivity Results for the Rényi-2 Entanglement of Purification [3.151184728006369]
  We show that for every completely positive map $N:L(B')to L(A)$, multiplicativity of $upsilon_p()$ implies multiplicativity for its complementary map.<n>This yields the corresponding additivity statements for the associated Rényi-2 entanglement of purification.
  arXiv  Detail & Related papers  (2026-05-14T21:41:31Z)
• Two-Indexed Schatten Quasi-Norms with Applications to Quantum Information Theory [9.048611509540079]
  We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces.<n>For linear maps between spaces of such quasi-norms, we introduce completely bounded quasi-norms and co-quasi-norms.<n>Our results imply a tensorizing notion of reverse hypercontractivity, additivity of the completely bounded minimum output Rényi-$$-entropy for $geqfrac12$ or the Sandwiched Rényi Umlaut information
  arXiv  Detail & Related papers  (2026-04-15T16:35:46Z)
• Rényi exponent landscape of multipartite entanglement in free-fermion systems [51.56484100374058]
  We show that the Rényi tripartite information $I_3() exhibits a qualitatively $exclusion-dependent scaling at small Fermi momentum.<n>A direct consequence is a replica obstruction: $I_m(n)/I_m(1) sim zm-1 to 0$ for all integer $n geq 2$, so the leading von Neumann signal cannot be reconstructed from integer Rényi data.
  arXiv  Detail & Related papers  (2026-03-09T22:27:00Z)
• Doubly minimized sandwiched Renyi mutual information: Properties and operational interpretation from strong converse exponent [0.0]
  We prove a novel duality relation for $alphain [frac23,infty]$ by employing Sion's minimax theorem.<n>We show that the doubly minimized sandwiched Renyi mutual information of order $alphain [1,infty]$ attains operational meaning in the context of binary quantum state discrimination.
  arXiv  Detail & Related papers  (2024-06-05T12:51:22Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• The quantum beam splitter with many partially indistinguishable photons: multiphotonic interference and asymptotic classical correspondence [44.99833362998488]
  We present the analysis of the quantum two-port interferometer in the $n rightarrow infty$ limit of $n$ partially indistinguishable photons. Our main result is that the output distribution is dominated by the $O(sqrtn)$ channels around a certain $j*$ that depends on the degree of indistinguishability. The form is essentially the doubly-humped semi-classical envelope of the distribution that would arise from $2 j*$ indistinguishable photons, and which reproduces the corresponding classical intensity distribution.
  arXiv  Detail & Related papers  (2023-12-28T01:48:26Z)
• Quantum Lower Bounds by Sample-to-Query Lifting [33.82353457014144]
  We propose a new method for proving quantum query lower bounds by a quantum sample-to-query lifting theorem.<n>We provide unified proofs for some known lower bounds, including those for phase/amplitude estimation and Hamiltonian simulation.
  arXiv  Detail & Related papers  (2023-08-03T14:41:49Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• Quantum Heavy-tailed Bandits [36.458771174473924]
  We study multi-armed bandits (MAB) and linear bandits (SLB) with heavy-tailed rewards and quantum reward. We first propose a new quantum mean estimator for heavy-tailed distributions, which is based on the Quantum Monte Carlo Estimator. Based on our quantum mean estimator, we focus on quantum heavy-tailed MAB and SLB and propose quantum algorithms based on the Upper Confidence Bound (UCB) framework.
  arXiv  Detail & Related papers  (2023-01-23T19:23:10Z)
• New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels [0.0]
  We present new families of quantum channels for which corresponding minimum output R'enyi $p$-entropy is not additive. Our manuscript is motivated by the results of Grudka et al., J. Phys. A: Math. Theor. 43 425304.
  arXiv  Detail & Related papers  (2023-01-18T10:55:30Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• A new parameterized entanglement monotone [3.267240600491982]
  Entanglement concurrence has been widely used for featuring entanglement in quantum experiments. We propose a new parameterized bipartite entanglement monotone named as $q$-concurrence inspired by general Tsallis entropy.
  arXiv  Detail & Related papers  (2021-01-12T01:38:55Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• Defining quantum divergences via convex optimization [12.462608802359936]
  We introduce a new quantum R'enyi divergence $D#_alpha$ for $alpha in (1,infty)$ defined in terms of a convex optimization program. An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum R'enyi divergence.
  arXiv  Detail & Related papers  (2020-07-24T15:28:44Z)
• Bosonic quantum communication across arbitrarily high loss channels [68.58838842613457]
  A general attenuator $Phi_lambda, sigma$ is a bosonic quantum channel that acts by combining the input with a fixed environment state. We show that for any arbitrary value of $lambda>0$ there exists a suitable single-mode state $sigma(lambda)$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity.
  arXiv  Detail & Related papers  (2020-03-19T16:50:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.