Related papers: Local Additivity Revisited
Entropic quantifiers of states lie at the cornerstone of the quantum information theory. While a quantum state can be abstracted as a device that only has outputs, the most general quantum device is a quantum channel that also has inputs.…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…
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 address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state. The second one is based on the relative entropy…
We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not…
An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…
Some new examples of quantum channels for which the infimum of the output entropy is additive under taking a tensor product of channels are given.
The primary entropic measures for quantum states are additive under the tensor product. In the analysis of quantum information processing tasks, the minimum entropy of a set of states, e.g., the minimum output entropy of a channel, often…
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…
We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local projective measurement on the qubit, which is valid for general entropic forms and becomes exact in…
We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal EPR pair distillation procedure for a given…
We study two complementary diagnostics of bipartite quantum channels, namely fidelity preservation across different classes of input states and entanglement generation from product inputs, given by properly defined entangling power for…
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…
It is shown that for real finite dimensional Hilbert spaces the additivity property of the minimum output entropy for quantum channels is always true.
We establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement. Our results pertain to the asymptotic limit of local manipulations on a large number of copies of…