Parameterized Multipartite Entanglement and Genuine Entanglement Measures Based on q-Concurrence.

We study genuine multipartite entanglement (GME) and multipartite k-entanglement based on q-concurrence. Well-defined parameterized GME measures and measures of multipartite k-entanglement are presented for arbitrary dimensional n-partite quantum systems. Our GME measures show that the GHZ state is more entangled than the W state. Moreover, our measures are shown to be inequivalent to the existing measures according to entanglement ordering. Detailed examples show that our measures characterize the multipartite entanglement finer than some existing measures, in the sense that our measures identify the difference of two different states while the latter fail.

Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA.

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality have turned out to be convex. Whether nonconvex entanglement measures obey the monogamy inequalities remains less known at present. As a well-known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the αth-power (α≥4ln2) of LCREN, and polygamy inequalities utilizing the αth-power (0≤α≤2) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high-dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions.

Battery Capacity of Energy-Storing Quantum Systems.

The quantum battery capacity is introduced in this Letter as a figure of merit that expresses the potential of a quantum system to store and supply energy. It is defined as the difference between the highest and the lowest energy that can be reached by means of the unitary evolution of the system. This function is closely connected to the ergotropy, but it does not depend on the temporary level of energy of the system. The capacity of a quantum battery can be directly linked with the entropy of the battery state, as well as with measures of coherence and entanglement.

Detecting genuine tripartite entanglement via general symmetric informationally complete measurements.

We study multipartite entanglement and genuine tripartite entanglement based on general symmetric informationally complete positive operator valued measurements (GSIC-POVMs). By representing the bipartite density matrices in terms of GSIC-POVMs, we obtain the lower bound of the sum of squares of the corresponding probability. We then construct a special matrix with the correlation probability of GSIC-POVMs to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. Detailed examples show that the new method can detect more entangled and genuine entangled states than previous criteria.

Assisted quantum simulation of open quantum systems.

Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits make the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of UQA via NISQ technology. Based on this framework, we present two quantum-assisted quantum algorithms for simulating open quantum systems, which utilize two parameterized quantum circuits to achieve a short-time evolution. We propose a variational quantum state preparation method, as a subroutine to prepare the ancillary state, for loading a classical vector into a quantum state with a shallow quantum circuit and logarithmic number of qubits. We demonstrate numerically our approaches for a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model on two sites.

Quantum Information and Computation.

Quantum technology can break through the bottleneck of traditional information technology by ensuring information security, speeding up computation, improving measurement accuracy, and providing revolutionary solutions to some issues of economic and social development [...].

Dynamics of Quantum Networks in Noisy Environments.

Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks.

Detecting Tripartite Steering via Quantum Entanglement.

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.

Blindly verifying partially unknown entanglement.

Quantum entanglement has shown distinguished features beyond any classical state. Many methods have been presented to verify unknown entanglement with the complete information about the density matrices by quantum state tomography. In this work, we aim to identify unknown entanglement with only partial information of the state space. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear entanglement witness expressed by density matrix elements. First, we verify unknown bipartite entanglement and study the robustness of entanglement witnesses against the white noise. Second, we generalize such verification to partially unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type and W-type states. Third, we give a quantum-information application related to the quantum zero-knowledge proof. It further provides a useful method in blindly verifying universal quantum computation resources. These results may be interesting in entanglement theories, quantum communication, and quantum networks.

A Characterization of Maximally Entangled Two-Qubit States.

As already known by Rana's result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [-12,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are -12. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is -12 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.