Measures of imaginarity and quantum state order

Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of quantum states based on l1 norm and convex functions in the framework of resource theory.Further,we investigate the quantum state order after a quantum system passes through a real channel.Rigorous proof shows that these proposed measures possess all the desirable properties for a measure of imaginarity.The connection between the measure of imaginarity based on the l1 norm and the measure of imaginarity based on relative entropy is derived.Moreover,we demonstrate that the l1 norm-based and the relative entropy-based measures of imaginarity are of the same order for qubit quantum states.Further we discuss the influences of the bit flip channel,phase damping channel,and amplitude flip channel on single qubit state order.

Separability criteria via some classes of measurements

Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs) and general symmetric informationally complete (GSIC) measurements, respectively, that are both not necessarily rank 1. We study the quantum separability problem by using these measurements and present separability criteria for bipartite systems with arbitrary dimensions and multipartite systems of multi-level subsystems. These criteria are proved to be more effective than previous criteria especially when the dimensions of the subsystems are different. Furthermore, full quantum state tomography is not needed when these criteria are implemented in experiment.

Block-coherence measures and coherence measures based on positive-operator-valued measures

We study block-coherence measures based on the resource theory of block-coherence and coherence measures based on positive-operator-valued measures(POVM).Several blockcoherence measures are presented,including the block-coherence measure based on maximum relative entropy,the one-shot block-coherence cost under maximally block-incoherent operations,and the coherence measure based on coherent rank.Their relationships are obtained.Moreover,we describe the deterministic coherence dilution process by constructing blockincoherent operations.Based on the POVM coherence resource theory,we also propose two coherence measures and analyze their relationship.

Transformations of multilevel coherent states under coherence-preserving operations

Quantum coherence,emerging from the"superposition"of quantum states,is widely used in various information processing tasks.Recently,the resource theory of multilevel quantum coherence is attracting substantial attention.In this paper,we mainly study the transformations of resource pure states via free operations in the theoretical framework for multilevel coherence.We prove that any two multilevel coherent resource pure states can be interconverted with a nonzero probability via a completely positive and trace non-increasing k-coherence-preserving map.Meanwhile,we present the condition of the interconversions of two multilevel coherent resource pure states under k-coherence-preserving operations.In addition,we obtain that in the resource-theoretic framework of multilevel coherence,no resource state is isolated,that is,given a multilevel coherent pure state|ψ>,there exists another multilevel coherent pure state|Φ>and a k-coherence-preserving operation∧k,such that∧k(|Φ>)=|ψ>.

Remote preparation for single-photon state in two degrees of freedom with hyper-entangled states

Remote state preparation(RSP)provides a useful way of transferring quantum information between two distant nodes based on the previously shared entanglement.In this paper,we study RSP of an arbitrary single-photon state in two degrees of freedom(DoFs).Using hyper-entanglement as a shared resource,our first goal is to remotely prepare the single-photon state in polarization and frequency DoFs and the second one is to reconstruct the single-photon state in polarization and time-bin DoFs.In the RSP process,the sender will rotate the quantum state in each DoF of the photon according to the knowledge of the state to be communicated.By performing a projective measurement on the polarization of the sender’s photon,the original single-photon state in two DoFs can be remotely reconstructed at the receiver’s quantum systems.This work demonstrates a novel capability for longdistance quantum communication.