On Partially Entanglement Breaking Channels

Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number for a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement.These classes generalize the well known class of entanglement breaking channels.     

Modulated entanglement evolution via correlated noises

We study entanglement dynamics in the presence of correlated environmental noises. Specifically, we investigate the quantum entanglement DYNAMics of two spins in the presence of correlated classical white noises, deriving Markov master equation and obtaining explicit solutions for several interesting classes of initial states including Bell states and X form density matrices. We show how entanglement can be enhanced or reduced by the correlation between the two participating noises.     

Quantum correlation via quantum coherence

Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition—quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes of quantum coherence. We propose a revised measure for total coherence and find that this measure can lead to a symmetric version of geometric quantum correlation, which is analytic for two qubits. In particular, this measure can also arrive at a monogamy equality on the distribution of quantum coherence. Finally, we also quantify a remaining type of quantum coherence and find that for two qubits, it is directly connected with quantum nonlocality.     

Concurrence and three-tangle of the graph

In this article, we study the entanglement properties of two-qubit quantum states based on concurrence using the graph-theoretic approach. Entanglement properties of a density operator are obtained from the combinatorial Laplacian matrix which is constructed for a given graph. In the study of entanglement, we found that measure of entanglement is either \( \frac{1}{ |{E}| } \) or zero for simple graphs. We further propose a simple method to evaluate the three-tangle and analyze inequivalent classes belonging to three-qubit pure states using graph-theoretic perspective. Our results allow a clear distinction between three-qubit separable states, genuinely entangled Greenberger–Horne–Zeilinger and W states, purely based on graphical interpretations.     

Entanglement-assisted quantum MDS codes from negacyclic codes

The entanglement-assisted formalism generalizes the standard stabilizer formalism, which can transform arbitrary classical linear codes into entanglement-assisted quantum error-correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we construct six classes of q-ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical negacyclic MDS codes by exploiting two or more pre-shared maximally entangled states. We show that two of these six classes q-ary EAQMDS have minimum distance more larger than \(q+1\). Most of these q-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.     

Distinguishing multipartite orthogonal product states by LOCC with entanglement as a resource

Recently, the method that using an entanglement as a resource to distinguish orthogonal product states by local operations and classical communication (LOCC) has brought into focus. Zhang et al. (Sci Rep 6:30493, 2016) presented protocols which use an entanglement to distinguish some classes of orthogonal product states in \(\mathbb {C}^m\otimes \mathbb {C}^n\). In this paper, we mainly study the local distinguishability of multipartite product states. For the class of locally indistinguishable multipartite product states constructed by Wang et al. (Quantum Inf Process 16:5, 2017), we present a protocol that distinguishes perfectly these quantum states by LOCC using an entangled state as a resource for implementing quantum measurements.     

Character of superposed states under deterministic LOCC

In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear superposition of states. For example, if we consider two pairs of incomparable states, then their superposition may result into a comparable pair of states. We investigate many such cases and provide some of the results in tabular form. We also investigate the entanglement behavior of such classes of states, specifically their monotone nature. Finally we provide some bounds of different measures of entanglement based on the idea of comparability and incomparability under deterministic LOCC.     

绝热量子搜索算法中的纠缠与能量分析

为了进一步研究量子纠缠与量子计算速度及能量的关系,通过计算von Neumann纠缠熵,分析了时间复杂度分别为O(N )和O(1)的绝热量子搜索算法的量子纠缠度随时间的变化关系,并对两者进行了比较.实验结果表明,量子纠缠对绝热量子计算的运行时间具有明显的影响,较大的纠缠可以导致更短的运行时间,反之亦然.同时对纠缠与能量的关系给出了一般性解释,即注入能量导致系统的纠缠增大,并因此缩短算法的运行时间.此外还分析了纠缠与量子系统初态的关系.实验表明系统初态形式不同,其纠缠度也不一样.初态为等幅叠加态的算法涉及的纠缠度明显大于初态为非等幅叠加态的算法.     

High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis

We investigate a novel quantum secret sharing (QSS) based on the Chinese remainder theory (CRT) in multi-dimensional Hilbert space with the orbital angular momentum (OAM) entanglement analysis. The secret is divided and then allotted to two or more participants who prepare pairs of photons in the OAM-entanglement states. The initial secret can be restored jointly by legal participants via the OAM-entanglement analysis on the corresponding photons. Its security is guaranteed from the OAM entanglement of photons that are established through the spin angular momentum (SAM) entanglement analysis performed on the generated SAM-based OAM hybrid entanglement photons. It provides an alternative technique for the QSS while producing the OAM entanglement photons in the combined multi-dimensional OAM Hilbert space, where the CRT is conducted properly for sharing the conventional secret among legal participants.     

Dualities and identities for entanglement-assisted quantum codes

The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is the code resulting from exchanging the original code’s information qubits with its ebits. To introduce this notion, we show how entanglement-assisted repetition codes and accumulator codes are dual to each other, much like their classical counterparts, and we give an explicit, general quantum shift-register circuit that encodes both classes of codes. We later show that our constructions are optimal, and this result completes our understanding of these dual classes of codes. We also establish the Gilbert–Varshamov bound and the Plotkin bound for EAQEC codes, and we use these to examine the existence of some EAQEC codes. Finally, we provide upper bounds on the block error probability when transmitting maximal-entanglement EAQEC codes over the depolarizing channel, and we derive variations of the hashing bound for EAQEC codes, which is a lower bound on the maximum rate at which reliable communication over Pauli channels is possible with the use of pre-shared entanglement.     

Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction

We study entanglement dynamics in two-parameter qubit–qutrit states under the influence of Dzyaloshisnhkii–Moriya (DM) interaction. Our system consists of a qubit–qutrit pair as a closed system initially in two-parameter class of states, and one environmental qubit interacts with the qutrit of the closed system via DM interaction. We divide our analysis into two cases. In the first case, we study the entanglement dynamics in separable region, and in the second case we study the same in non-separable region. The DM interaction produces the entanglement in separable region with entanglement sudden death (ESD) and some states in this region remain unaffected by the same. In non-separable region, all the states are affected by DM interaction. The DM interaction excites the entanglement but does not produce ESD in this region. We observed that probability amplitude of environmental qubit does not affect the entanglement in two-parameter qubit–qutrit states in both the regions.     

Asymptotic entanglement in quantum walks from delocalized initial states

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.     

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW??s are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance.     

The Correlation Conversion property of quantum channels

Transmission of quantum entanglement will play a crucial role in future networks and long-distance quantum communications. Quantum key distribution, the working mechanism of quantum repeaters and the various quantum communication protocols are all based on quantum entanglement. On the other hand, quantum entanglement is extremely fragile and sensitive to the noise of the communication channel over which it has been transmitted. To share entanglement between distant points, high fidelity quantum channels are needed. In practice, these communication links are noisy, which makes it impossible or extremely difficult and expensive to distribute entanglement. In this work, we first show that quantum entanglement can be generated by a new idea, exploiting the most natural effect of the communication channels: the noise itself of the link. We prove that the noise transformation of quantum channels that are not able to transmit quantum entanglement can be used to generate distillable (useable) entanglement from classically correlated input. We call this new phenomenon the Correlation Conversion property of quantum channels. The proposed solution does not require any non-local operation or local measurement by the parties, only the use of standard quantum channels. Our results have implications and consequences for the future quantum communications and for global-scale quantum communication networks. The discovery also revealed that entanglement generation by local operations is possible.     

Tripartite entanglement of a spin star model with Dzialoshinski–Moriya interaction

The effect of Dzialoshinski–Moriya (DM) interaction on the tripartite thermal entanglement of a spin-star model with four spins has been analyzed by an entanglement measure of the tripartite negativity. Our results imply that the tripartite thermal entanglement can be established among the three surrounding parties which do not interact with each other but interact with the central party independently. From the results, we find that the strong DM interaction can enhance the tripartite thermal entanglement while the high temperature can shrink it. The effect of the inhomogeneous coupling on the tripartite thermal entanglement is also discussed.     

Bell state entanglement swappings over collective noises and their applications on quantum cryptography

This work presents two robust entanglement swappings against two types of collective noises, respectively. The entanglement swapping can be achieved by performing two Bell state measurements on two logical qubits that come from two original logical Bell states, respectively. Two fault tolerant quantum secret sharing (QSS) protocols are further proposed to demonstrate the usefulness of the newly proposed entanglement swappings. The proposed QSS schemes are not only free from Trojan horse attacks but also quite efficient. Moreover, by adopting two Bell state measurements instead of four-qubit joint measurements, the proposed protocols are practical in combating collective noises. The proposed fault tolerant entanglement swapping can also be used to replace the traditional Bell-state entanglement swapping used in various quantum cryptographic protocols to provide robustness in combating collective noises.     

Entanglement sudden death and birth in qubit–qutrit systems under Dzyaloshinskii–Moriya interaction

We study entanglement dynamics of qubit–qutrit pair under Dzyaloshinskii–Moriya (DM) interaction. The qubit–qutrit pair acts as a closed system and one external qubit serve as the environment for the pair. The external qubit interact with qubit of closed system via DM interaction. This interaction frequently kills the entanglement between qubit–qutrit pair, which is also periodically recovered. On the other hand two parameter class of state of qubit–qutrit pair also affected by DM interaction and one parameter class of state remains unaffected. The frequency of occurrence of entanglement sudden death and entanglement sudden birth in two parameter class of state is half than qubit–qutrit pure state. We used our quantification of entanglement as negativity measure.     

Nuclear polarization and entanglement in spin systems

We investigated relationships between entanglement measures and the order parameter (nuclear polarization) in nuclear spin systems controlled by the nuclear magnetic resonance (NMR) technique. Since spin polarization can be easily manipulated by the NMR technique, experimentalists are presented with an opportunity to study the dynamic properties of entanglement, i.e., the creation and evolution of entangled states. Our approach may constitute the basis for researching the relations between the entanglement measures and measurable parameters of order in other quantum systems. An erratum to this article can be found at