We correct a mistake in a result reported in [PRA 64, 062106 (2001)], where it is rightfully argued that initial correlations between a system and its environment may render the system reduced dynamics not completely positive. We prove how not only these initial correlations but also the specific joint dynamics does play a significant role in the question of the complete positivy of the reduced dynamics.
The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for both theoretical and practical reasons. As LOCC has a highly intricate structure, sometimes the larger set of separable (SEP) maps is considered, which has a mathematically much simpler description. In the literature, mainly SEP maps consisting of invertible Kraus operators have been taken into account. In this paper we show that the consideration of those maps is not sufficient when deciding whether a state c…
Multipartite entanglement has been shown to be of particular relevance for a better understanding and exploitation of the dynamics and flow of entanglement in multiparty systems. This calls for analysis aimed at identifying the appropriate processes that guarantee the emergence of multipartite entanglement in a wide range of scenarios. Here we carry on such analysis considering a system of two initially entangled qubits, one of which is let to interact with a third qubit according to an arbitrary unitary evolution. We establish necessary and sufficient conditions on the corresponding Kraus ope…
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed third-order differential equation with all the higher-order environmental correlations taken into account and the reduced density matrix of the two qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two qubit syst…
Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator model -- a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling, where the bath oscillator is initially in a thermal-like state. In particular, we treat the completely positive and trace preserving map on the system as a quantum channel, and study the truncation of the channel by truncating its Kraus set and its outp…
Schemes for topological quantum computation are usually based on the assumption that the system is initially prepared in a specific state. In practice, this state preparation is expected to be challenging as it involves non-topological operations which heavily depend on the experimental realization and are not naturally robust against noise. Here we show that this assumption can be relaxed by using composite anyons: starting from an unknown state with reasonable physical properties, it is possible to efficiently distill suitable initial states for computation purely by braiding. This is achiev…
Trainable Quantum Channels as Computational Primitives for Quantum Learning
China Mobile (Suzhou) Software Technology Company Limited（中国移动（苏州）软件技术有限公司）；QuSpect Technology Company Limited（QuSpect科技有限公司）；School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；Frontier Science Center for Quantum Information（量子信息前沿科学中心）
Beyond Gaussian Entanglement: Practical Criteria for Polynomially Excited Quantum States
HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳物理研究中心）；HUN-REN Alfréd Rényi Institute of Mathematics（匈牙利科学院阿尔弗雷德·雷尼数学研究所）；Institute of Mathematics and Informatics, Eszterházy Károly Catholic University（埃斯泰尔戈姆卡洛天主教大学数学与信息研究所）；Institute of Mathematics and Informatics, Faculty of Science, University of Pécs（佩奇大学理学院数学与信息研究所）；Department of Physics of Complex Systems, Eötvös Loránd University（罗兰大学复杂系统物理系）
