Related papers: Counterexamples to the maximal p-norm multiplicati…
The von Neumann entropy of a quantum state is a central concept in physics and information theory, having a number of compelling physical interpretations. There is a certain perspective that the most fundamental notion in quantum mechanics…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum…
Additivity of minimal entropy output is proven for the class of quantum channels $\Lambda_t (A):=t A^{T}+(1-t)\tau (A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.
We prove additivity violation of minimum output entropy of quantum channels by straightforward application of \epsilon-net argument and L\'evy's lemma. The additivity conjecture was disproved initially by Hastings. Later, a proof via…
Recently, King and Ruskai [1] conjectured that the maximal p-norm of the Werner--Holevo channel is multiplicative for all $1\le p \le 2$. In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity…
Capacities of quantum channels are fundamental quantities in the theory of quantum information. A desirable property is the additivity for a capacity. However, this cannot be achieved for a few quantities that have been established as…
It is shown that for real finite dimensional Hilbert spaces the additivity property of the minimum output entropy for quantum channels is always true.
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…
When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity -- a fundamental synergy which…
The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher…
Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood…
We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of…
Using the graphical calculus and integration techniques introduced by the authors, we study the statistical properties of outputs of products of random quantum channels for entangled inputs. In particular, we revisit and generalize models…
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…
In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…
We give a simple and conceptual proof of the fact that random unitary channels yield violation of the Minimum Output Entropy additivity. The proof relies on strong convergence of random unitary matrices and Haagerup's inequality.
We generalize recent results of Collins and Youn (2022), presenting new classes of quantum channels violating the additivity of the regularized minimum output entropy in the commuting-operator setup.
We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order $\alpha\in[\frac{1}{2},1)$. To prove this, we introduce…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…