We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations) any state chosen from the set of two-colorable graph states (CSS codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.
We propose two deterministic secure quantum communication (DSQC) protocols employing three-qubit GHZ-like states and five-qubit Brown states as quantum channels for secure transmission of information in units of two bits and three bits using multipartite teleportation schemes developed here. In these schemes, the sender's capability in selecting quantum channels and the measuring bases leads to improved qubit efficiency of the protocols.
"Quantum conversation" is a way in which two parties can communicate classical information with each other using entanglement as a shared resource. We present this scheme using a multipartite entangled state after describing its generation through appropriate circuit diagrams. We make use of a discrimination scheme which allows one to perform a measurement on the system without destroying its entanglement. We later prove that this scheme is secure in a noiseless and a lossless quantum channel.
We consider the problem of secure key distribution among $n$ trustful agents: the goal is to distribute an identical random bit-string among the $n$ agents over a noisy channel such that eavesdroppers learn little about it. We study the general situation where the only resources required are secure bipartite key distribution and authenticated classical communication. Accordingly, multipartite quantum key distribution can be proven unconditionally secure by reducing the problem to the biparitite case and invoking the proof of security of bipartite quantum key distribution.
Entanglement plays a crucial role in the security of quantum key distribution. A secret key can only be obtained by two parties if there exists a corresponding entanglement-based description of the protocol in which entanglement is witnessed, as shown by Curty et al (2004). Here we investigate the role of entanglement for the generalization of quantum key distribution to the multipartite scenario, namely conference key agreement. In particular, we ask whether the strongest form of multipartite entanglement, namely genuine multipartite entanglement, is necessary to establish a conference key. W…
We present a composably secure protocol allowing $n$ parties to test an entanglement generation resource controlled by a possibly dishonest party. The test consists only in local quantum operations and authenticated classical communication once a state is shared among them and provides composable security, namely it can be used as a secure subroutine by $n$ honest parties within larger communication protocols to test if a source is sharing quantum states that are at least $ε$-close to the GHZ state. This claim comes on top of previous results on multipartite entanglement verification where the…
Superdense coding uses entanglement as a resource to communicate classical information securely through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we have demonstrated a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary informat…
It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on distillable cryptographic key in bipartite scenario.
We construct multipartite entangled states with underlying W-type structure satisfying positive partial transpose (PPT) condition under any (N-1)|1 partition. Then we show how to distill N-partite secure key form the states using two different methods: direct application of local filtering and novel random key distillation scheme in which we adopt the idea form recent results on entanglement distillation. Open problems and possible implications are also discussed.
Users of quantum networks can securely communicate via so-called (quantum) conference key agreement --making their identities publicly known. In certain circumstances, however, communicating users demand anonymity. Here, we introduce a security framework for anonymous conference key agreement with different levels of anonymity, which is inspired by the epsilon-security of quantum key distribution. We present efficient and noise-tolerant protocols exploiting multipartite Greenberger-Horne-Zeilinger (GHZ) states and prove their security in the finite-key regime. We analyze the performance of our…
Motivated by the recent studies on post-quantum steering, we generalize the notion of bipartite channel steering by introducing the concept of multipartite no-signaling channel assemblages. We first show that beyond the bipartite case, the no-signaling and quantum descriptions of channel assemblages do not coincide. Using the Choi-Jamiołkowski isomorphism, we present a complete characterization of these classes of assemblages and use this characterization to provide sufficient conditions for extremality of quantum channel assemblages within the set of all no-signaling channel assemblages. Fina…
We propose a new quantum secret sharing scheme using a single non-entangled qubit. In the scheme, by transmitting a qubit to the next party sequentially, a sender can securely transmit a secret message to $N$ receivers who could only decode the message cooperatively after randomly shuffling the polarization of the qubit. We explain this quantum secret sharing scheme into the one between a sender and two receivers, and generalize the scheme between a sender and $N$ receivers. Since our scheme is capable of using a faint coherent pulse as a qubit, it is experimentally feasible within current tec…
Multipartite entangled states are a fundamental resource for a wide range of quantum information processing tasks. In particular, in quantum networks it is essential for the parties involved to be able to verify if entanglement is present before they carry out a given distributed task. Here we design and experimentally demonstrate a protocol that allows any party in a network to check if a source is distributing a genuinely multipartite entangled state, even in the presence of untrusted parties. The protocol remains secure against dishonest behaviour of the source and other parties, including …
This paper examines the coherence in multipartite systems. We first discuss the distribution of total coherence in a given multipartite quantum state into discord between subsystems and coherent dissonance in each individual subsystem, using the relative entropy as a distance measure. Then we give some trade-off relations between various types of coherence and discord within a bipartite system,and extend these results to the multipartite setting. Finally, the change of coherence in entanglement distribution is studied.
Future quantum information networks will likely consist of quantum and classical agents, who have the ability to communicate in a variety of ways with trusted and untrusted parties and securely delegate computational tasks to untrusted large-scale quantum computing servers. Multipartite quantum entanglement is a fundamental resource for such a network and hence it is imperative to study the possibility of verifying a multipartite entanglement source in a way that is efficient and provides strong guarantees even in the presence of multiple dishonest parties. In this work, we show how an agent o…
We present a scheme to generate a continuous variable (CV) multipartite entangled state using an array of plasmonic graphene waveguides that are activated by nonclassical driving microwave modes. Within this scheme, we can exploit the interaction of two light fields coupled to the same microwave mode in each waveguide to produce any type of multipartite Gaussian entangled state. A teleportation network is illustrated using the resultant CV multipartite entangled state. In particular, the proposed setup enables coherent state teleportation across remotely connected nodes with fidelity above a t…
Absolutely and asymptotically secure protocols for organizing an exam in a quantum way are proposed basing judiciously on multipartite entanglement. The protocols are shown to stand against common types of eavesdropping attack.
Einstein-Podolsky-Rosen (EPR) steering is the explicit demonstration of the fact that the measurements of one party can in influence the quantum state held by another, distant, party, and do so even if the measurements themselves are untrusted. This has been shown to allow one-sided device-independent quantum-information tasks between two remote parties. However, in general, advanced multiparty protocols for generic quantum technologies, such as quantum secret sharing and blind quantum computing for quantum networks, demand multipartite quantum correlations of graph states shared between more …
Quantum secret sharing (QSS) is an essential primitive for the future quantum internet, which promises secure multiparty communication. However, developing a large-scale QSS network is a huge challenge due to the channel loss and the requirement of multiphoton interference or high-fidelity multipartite entanglement distribution. Here, we propose a three-user QSS protocol without monitoring signal disturbance, which is capable of ensuring the unconditional security. The final key rate of our protocol can be demonstrated to break the Pirandola-Laurenza-Ottaviani-Banchi bound of quantum channel a…
We present a convenient and efficient way to exchange and distribute multipartite entangled state via atomic coherence induced by electromagnetically induced transparency (EIT) in an atomic ensemble. By using the EIT-based nondegenerate four-wave mixing processes, the generation, exchange, and distribution of light-light, atom-light, and atom-atom multipartite entanglement can be achieved in a deterministic way with only coherent light fields. This EIT-induced atomic coherence acts as a quantum information processor and has the function of quantum beam splitter, quantum frequency converter, qu…
We investigate the distribution property of one way discord in multipartite system by introducing the concept of polygamy deficit for one way discord. The difference between one way discord and quantum discord is analogue to the difference between entanglement of assistance and entanglement of formation. For tripartite pure states, two kinds of polygamy deficits are presented with the equivalent expressions and physical interpretations regardless of measurement. For four-partite pure states, we provide a condition which makes one way discord polygamy being satisfied. Those results can be appli…
We propose a scheme for multiparty hierarchical quantum-information splitting (QIS) with a multipartite entangled state, where a boss distributes a secret quantum state to two grades of agents asymmetrically. The agents who belong to different grades have different authorities for recovering boss's secret. Except for boss's Bell-state measurement, no nonlocal operation is involved. The presented scheme is also shown to be secure against eavesdropping. Such a hierarchical QIS is expected to find useful applications in the field of modern multipartite quantum cryptography.
For a two-qubit state the isotropic strength measures the degree of isotropic spin correlation. The concept of isotropic strength is generalized to multipartite qudit systems, and the strength distributions for tripartite and quadripartite qudit systems are thoroughly investigated. We show that the sum of relative isotropic strengths of any three qudit state over $d$-dimensional Hilbert space cannot exceed $d-1$, which generalizes of the case $d=2$. The trade-off relations and monogamy-like relations of the sum of spin correlation strengths for pure three- and four-partite systems are derived.…
We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of mu…
Quantum secret sharing is well known as a method for players to share a classical secret for secret sharing in quantum mechanical ways. Most of the results associated with quantum secret sharing are based on pure multipartite entangled states. In reality, however, it is difficult for players to share a pure entangled state, although they can share a state close to the state. Thus, it is necessary to study how to perform the quantum secret sharing based on a general multipartite state. We here present a quantum secret sharing protocol on an $N$-qubit state close to a pure $N$-qubit Greenberger-…
Distribution of quantum correlations among remote users is a key procedure underlying many quantum information technologies. Einstein-Podolsky-Rosen steering, which is one kind of such correlations stronger than entanglement, has been identified as a resource for secure quantum networks. We show that this resource can be established between two and even more distant parties by transmission of a system being separable from all the parties. For the case with two parties, we design a protocol allowing to distribute one-way Gaussian steering between them via a separable carrier; the obtained steer…
We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytic upper bound for the concurrence of assistance in bipartite quantum systems, and derive a polygamy inequality of multipartite entanglement in arbitrary dimensional quantum systems.
The ability to reliably distribute entanglement among the nodes of a network is an essential requirement for the development of effective quantum communication protocols and the realization of useful quantum networks. It has been demonstrated, in different contexts, that two remote systems can be entangled via local interactions with a carrier system that always remains in a separable state with respect to such distant particles. We develop a strategy for entanglement distribution via separable carriers that can be applied to any number of network nodes to achieve various entanglement distribu…
We investigate the average bipartite entanglement, over all possible divisions of a multipartite system, as a useful measure of multipartite entanglement. We expose a connection between such measures and quantum-error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states. Multipartite entangling power of quantum evolutions is also investigated.
We study the performance (rate and fidelity) of distributing multipartite entangled states in a quantum network through the use of a central node. Specifically, we consider the scenario where the multipartite entangled state is first prepared locally at a central node, and then transmitted to the end nodes of the network through quantum teleportation. As our first result, we present leading-order analytical expressions and lower bounds for both the rate and fidelity at which a specific class of multipartite entangled states, namely Greenberger-Horne-Zeilinger (GHZ) states, are distributed. Our…
We present a multipartite nonlocal game in which each player must guess the input received by his neighbour. We show that quantum correlations do not perform better than classical ones at this game, for any prior distribution of the inputs. There exist, however, input distributions for which general no-signalling correlations can outperform classical and quantum correlations. Some of the Bell inequalities associated to our construction correspond to facets of the local polytope. Thus our multipartite game identifies parts of the boundary between quantum and post-quantum correlations of maximal…
A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.
The distribution of coherence in multipartite systems in examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or distributed among the sites, which contribute in a complementary…
Multipartite cryptography is useful for some particular missions. In this paper, we present a quantum key distribution scheme in which three separated observers can securely share a set of keys by using a sequence of $3$-particle GHZ states. We prove that the violation of Svetlichny's inequality can be utilized to test for eavesdropping, and even when the eavesdropper can completely control the outcomes of two participants' measurements, our scheme still ensures the security of the keys distribution. This scheme can be easily extended to the case of $N$-party keys distribution, and the violati…
Quantum network applications like distributed quantum computing and quantum secret sharing present a promising future network equipped with quantum resources. Entanglement generation and distribution over long distances is critical and unavoidable to utilize quantum technology in a fully-connected network. The distribution of bipartite entanglement over long distances has seen some progresses, while the distribution of multipartite entanglement over long distances remains unsolved. Here we report a two-dimensional quantum repeater protocol for the generation of multipartite entanglement over l…
Using the relative entropy of total correlation, we derive an expression relating the mutual information of $n$-partite pure states to the sum of the mutual informations and entropies of its marginals and analyze some of its implications. Besides, by utilizing the extended strong subadditivity of von Neumann entropy, we obtain generalized monogamy relations for the total correlation in three-partite mixed states. These inequalities lead to a tight lower bound for this correlation in terms of the sum of the bipartite mutual informations. We use this bound to propose a measure for residual three…
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state …
Correlations play a key role in critical phenomena. Quantities such as the entanglement entropy, for instance, provide key insights into the mechanisms underlying quantum criticality. Almost all of our present knowledge, however, is restricted to bipartite correlations. Some questions still remain unanswered, such as: What parcel of the total correlations are genuinely k-partite? With the goal of shedding light on this difficult question, in this paper we put forth a detailed study of the behavior of genuine multipartite correlations (GMC) of arbitrary orders in the Lipkin-Meshkov-Glick model.…
Quantum chaotic maps can efficiently generate pseudo-random states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the system. We show that such multipartite entanglement is robust, in the sense that, when realistic noise is considered, distillable entanglement of bipartitions remains almost maximal up to a noise strength that drops only polynomially with the number of qubits.
In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or carry out public classical communication. These ``secrecy monotones'' therefore measure how much secret correlations are shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalisations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monot…
We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts a quantifier of genuine multipartite steering, and is interpreted operationally in terms of…
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C, the entanglement of formation E, negativity Nc and Tsallis-q entanglement Tq. Monogamy relations for the $α$th power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.
We develop a protocol based on 2M pairwise interacting qubits, which through Quantum Zeno Effect controls the entanglement distribution of the system. We also show that if the coupling constants are different the QZE may be used to achieve perfect entanglement swap.
The distribution of quantum correlations in multipartite systems play a significant role in several aspects of the quantum information theory. While it is well known that these quantum correlations can not be freely distributed, the way that it is shared in multipartite system is an open problem even for small set of qubits. Based on new monogamylike relations between entanglement and discord for $n$-partite systems, we show how these correlations are distributed in general, determining distinct equalities and inequalities to the quantum discord and the entanglement of formation for arbitrary …
