Improved characterization of quantum states for quantum information

Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr

Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based on generalized divergences and prove their invariance under local isometric or unitary transformations. Leveraging the reversal channel for local isometries together with the data-processing inequality, we establish invariance for information quantities used in both asymptotic and one-shot regimes without relying on the specific functional form of the underlying divergence. These invariances can be applied to improve the computation of such information quantities or optimize protocols and their output states, whose performance is determined by some invariant measure. Our results improve the capability to characterize and compute many operationally relevant information measures with application across the field of quantum information processing.

Miroslav Svítek

Yonghae Lee, Joonwoo Bae, Hayata Yamasaki +1 more

Abstract In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages required to be exchanged to completely share all information in common. However, this equivalence does not extend to quantum information theory. Specifically, quantum uncommon information (QUI) is operationally defined as the minimal amount of entanglement required for the quantum communication task of quantum state exchange (QSE), where two parties exchange quantum states to share all quantum messages in common. Currently, an analytical closed-form expression for the QUI remains undetermined. In this work, by investigating underlying characterization of the QUI, we derive improved bounds on it. To obtain these bounds, we develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. We also consider a referee-assisted exchange, wherein a referee aids two parties in efficiently performing the QSE. Our bounds provide more precise estimations for the QUI. Furthermore, we demonstrate that the subspace technique is a versatile tool for characterizing uncommon information not only in the bipartite scenario but also in various multi-partite ones.

Alessia Suprano, Taira Giordani, Emanuele Polino +10 more

The capability to engineer and characterize high dimensional states has become a crucial request in the quantum information field. The quantum walk dynamics proved to be a suitable resource for developing general quantumstate engineering protocols. Here, we experimentally verified the flexibility of an engineering protocol based on a one-dimensional quantum walk in the Orbital Angular Momentum (OAM). Although this degree of freedom has found several applications in the quantum information field, extract the information stored in them appears to be difficult. Therefore, we employ machine learning protocols to classify and characterize particularly structured beams endowed with a not uniform distribution of the polarization on the transverse plane. Moreover, we prove that by modeling the engineering process through a refined model it is possible to improve the performances of measurement techniques such as holographic projection and machine-learning based classification. These results represent a further investigation in the manipulation and detection of OAM modes coupling the photonics platforms with machine-learning protocols.

Marco Tomamichel