The usefulness of the genuinely entangled six qubit state that was recently introduced by Borras et al. is investigated for the quantum teleportation of an arbitrary three qubit state and for quantum state sharing (QSTS) of an arbitrary two qubit state. For QSTS, we explicitly devise two protocols and construct sixteen orthogonal measurement basis which can lock an arbitrary two qubit information between two parties.
We put forward a simple construction of genuinely entangled subspaces -- subspaces supporting only genuinely multipartite entangled states -- of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a g…
Building upon the results of [R. Augusiak et al., Phys. Rev. Lett. 115, 030404 (2015)] we develop a general approach to the generation of genuinely entangled multipartite states of any number of parties from genuinely entangled states of a fixed number of parties, in particular, the bipartite entangled ones. In our approach, certain isometries whose output subspaces are either symmetric or genuinely entangled in some multipartite Hilbert spaces are applied to local subsystems of bipartite entangled or multipartite genuinely entangled quantum states. To prove that entanglement of the resulting …
Genuinely entangled subspaces are a class of subspaces in the multipartite Hilbert spaces that are composed of only genuinely entangled states. They are thus an interesting object of study in the context of multipartite entanglement. Here we provide a construction of multipartite subspaces that are not only genuinely entangled but also fully non-positive-partial-transpose (NPT) in the sense that any mixed state supported on them has non-positive partial transpose across any bipartition. Our construction originates from the stabilizer formalism known for its use in quantum error correction. To …
Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure state. Among CESs one finds a class of subspaces in which all vectors are not only entangled, but are genuinely entangled. Here we explore the connection between UPBs…
Recently, Ri-Gui Zhou et al. [Int. J. Theor. Phys. 59, 166-172 (2020)] proposed a scheme for bidirectional quantum teleportation of two-two and two-three qubit states by utilizing a six-qubit entangled state as a quantum channel. It is observed that the intrinsic efficiency calculated by Zhou et al. is not correct. In this improved scheme, we show that bidirectional teleportation of two-two and two-three qubit quantum states can be done by using optimized quantum resource and less consumption of classical resource. We also calculate the intrinsic efficiency of our improved scheme which is much…
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces -- the class of subspaces consisting entirely of genuinely multipartite entangled pure states. In this paper we present several methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the correspondence betwe…
We study the efficacy of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separa…
Three-qubit mixed states are used as a channel for controlled quantum teleportation (CQT) of single-qubit states. The connection between different channel parameters to achieve maximum controlled teleportation fidelity is investigated. We show that for a given multipartite entanglement and mixedness, a class of non-maximally entangled mixed $X$ states ($X-$NMEMS) achieves optimum controlled quantum teleportation fidelity, interestingly a class of maximally entangled mixed $X$ states ($X-$MEMS) fails to do so. This demonstrates, for a given spectrum and mixedness, that $X-$MEMS are not sufficie…
We show that there are six inequivalent $4\times4$ unextendible product bases (UPBs) of size eight, when we consider only 4-qubit product vectors. We apply our results to construct Positive-Partial-Transpose entangled states of rank nine. They are at the same 4-qubit, $2\times2\times4$ and $4\times4$ states, and their ranges have product vectors. One of the six UPBs turns out to be orthogonal to an almost genuinely entangled space, in the sense that the latter does not contain $4\times4$ product vector in any bipartition of 4-qubit systems. We also show that the multipartite UPB orthogonal to …
Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using pre-shared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and prov…
We constructed a class of non-maximally entangled mixed states \cite{roy2010} and extensively studied its entanglement properties and also their usefulness as teleportation channels. In this article, we revisited our constructed state and have studied it from three different perspectives. Since every entangled state is associated with an witness operator, we have found a suitable entanglement as well as teleportation witness for our non-maximally entangled mixed states. We considered the noisy channel's effects on our constructed state and to see whether it affects the states' capacity as tele…
We consider the problem of bi-directional controlled quantum teleportation of information encoded in phase opposite coherent state among two distant partners Alice and Bob, with the consent of controller, Charlie. We use five-mode cluster-type entangled coherent state as the quantum resource to achieve this task. The scheme uses linear optical devices such as beam splitter, phase shifters, and photon counters. We have shown that for moderately large coherent amplitude, near-perfect bi-directional controlled teleportation can be obtained in terms of the average fidelity of teleportation.
The relation of genuine multiqubit entanglement and controlled teleportation
最近，Paolo Facchi等人[Phys. Rev. A. 77，060304（R）（2008）]引入了n个量子比特的最大多体纠缠态的概念。本文给出了通过五量子比特纠缠态实现任意两量子比特态的忠实受控隐形传态的判据，并得到了真实五量子比特纠缠态与受控隐形传态之间的一般关系.该判据可以推广到利用2N+1量子比特纠缠态隐形传送任意N量子比特态。进一步研究了测量基与量子信道的最佳匹配。
Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified prot…
We investigate genuinely entangled $N$-qubit states with no $N$-partite correlations in the case of symmetric states. Using a tensor representation for mixed symmetric states, we obtain a simple characterization of the absence of $N$-partite correlations. We show that symmetric states with no $N$-partite correlations cannot exist for an even number of qubits. We fully identify the set of genuinely entangled symmetric states with no $N$-partite correlations in the case of three qubits, and in the case of rank-2 states. We present a general procedure to construct families for an arbitrary odd nu…
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of bipartite entangled subspaces under joining of their adjacent subsystems. In addition, it is shown that direct sums of such constructions under certain conditions are genuinely entangled. These facts are then used in detecting entanglement of tensor products of mixed states and constructing subspaces that are distillable across every bipartite cut, where for…
As a variant of the original quantum teleportation, the port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of the ports. We here consider a generalization of …
The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown however that all entangled states lead to non-classical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand we demonstrate that every entangled state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlat…
Quantum entanglement is a fundamental resource for quantum information processing and is widely used in quantum communication, quantum computation and quantum metrology. Early research on quantum entanglement mainly focus on qubit states, but in recent years, more and more research has begun to focus on high-dimensional entangled states. Compared with qubit entangled states, higher-dimensional entangled states have a larger information capacity and the potential to realize more complex quantum applications. In this Letter, we have experimentally prepared a special high-dimensional entangled st…
Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of state self-testing has been generalized to entangled subspaces and the first self-testing strategies for exemplary genuinely entangled subspaces have been given. The main aim of our work is to pursue this line of research and to address the question how "large" (in terms of dimension) are genuinely entangled subspaces that can be self-tested, concentrating on the mul…
