Related papers: Quantum conditional mutual information and approxi…
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In…
We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs…
If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum…
A tripartite state $\rho_{ABC}$ forms a Markov chain if there exists a recovery map $\mathcal{R}_{B \to BC}$ acting only on the $B$-part that perfectly reconstructs $\rho_{ABC}$ from $\rho_{AB}$. To achieve an approximate reconstruction, it…
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite…
A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual…
The connection between quantum state recovery and quantum conditional mutual information (QCMI) is studied for the class of purely generated finitely correlated states (pgFCS) of one-dimensional quantum spin chains. For a tripartition of…
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be…
Quantum conditional mutual information (QCMI) is a versatile information theoretic measure. It is used to find the amount of correlations between two qubits from the perspective of a third qubit. In this work we characterise the QCMI of…
A short quantum Markov chain is a tripartite state $\rho_{ABC}$ such that system $A$ can be recovered perfectly by acting on system $C$ of the reduced state $\rho_{BC}$. Such states have conditional mutual information $I(A;B|C)$ equal to…
A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically, relating the conditional mutual information to a commutator is a very promising approach…
We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined…
We introduce and analyze a task that we call Markovianization, in which a tripartite quantum state is transformed to a quantum Markov chain by a randomizing operation on one of the three subsystems. We consider cases where the initial state…
Quantum Markov chains generalize classical Markov chains for random variables to the quantum realm and exhibit unique inherent properties, making them an important feature in quantum information theory. In this work, we propose the concept…
We study the relation between the quantum conditional mutual information and the quantum $\alpha$-R\'enyi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the…
A state on a tripartite quantum system $\mathcal{H}_{A}\otimes \mathcal{H}_{B}\otimes\mathcal{H}_{C} $ forms a Markov chain, i.e., quantum conditional independence, if it can be reconstructed from its marginal on $\mathcal{H}_{A}\otimes…
In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our…
We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the…
It is well-known that the conditional mutual information of a quantum state is zero if, and only if, the quantum state is a quantum Markov chain. Replacing the Umegaki relative entropy in the definition of the conditional mutual information…
We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$…