We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an $N$-partite version of the BB84 protocol and we discuss the $N$-partite six-state protocol proposed in arXiv:1612.05585v2. The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.
We present a tripartite three-level state that allows a secret sharing protocol among the three parties, or a quantum key distribution protocol between any two parties. The state used in this scheme contains entanglement even after one system is traced out. We show how to utilize this residual entanglement for quantum key distribution purposes, and propose a realization of the scheme using entanglement of orbital angular momentum states of photons.
The problem of noise incidence on qubits taking part of bipartite entanglement-based protocols is addressed. It is shown that the use of a three-partite GHZ state and measurements instead of their EPR counterparts allows the experimenter to detect $2/3$ of the times whenever one of the qubits involved in the measurement is affected by bit-flip noise through the mere observation of unexpected outcomes in the teleportation and superdense coding protocols when compared to the ideal case. It is shown that the use of post-selection after the detection of noise leads to an enhancement in the efficie…
The laws of quantum mechanics allow for the distribution of a secret random key between two parties. Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement. We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates. Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network c…
We propose a wide class of distillation schemes for multi-partite entangled states that are CSS-states. Our proposal provides not only superior efficiency, but also new insights on the connection between CSS-states and bipartite graph states. We then apply our distillation schemes to the tri-partite case for three cryptographic tasks--namely, (a) conference key agreement, (b) quantum sharing of classical secrets and (c) third-man cryptography. Moreover, we construct ``prepare-and-measure'' protocols for the above three cryptographic tasks which can be implemented with the generation of only a …
We develop protocols for preparing a GHZ state and, in general,a pure multi-partite maximally entangled state in a distributed network with apriori quantum entanglement between agents using classical communication and local operations. We investigate and characterize the minimal combinatorics of the sharing of EPR pairs required amongst agents in a network for the creation of multi-partite entanglement. We also characterize the minimal combinatorics of agents in the creation of pure maximal multi-partite entanglement amongst the set $N$ of $n$ agents in a network using apriori multi-partite en…
We provide various schemes for the splitting up of Quantum information into parts using the four and five partite cluster states. Explicit protocols for the Quantum information splitting (QIS) of single and two qubit states are illustrated. It is found that the four partite cluster state can be used for the QIS of an entangled state and the five partite cluster state can be used for QIS of an arbitrary two qubit state. The schemes considered here are also secure against certain eavesdropping attacks.
Secret sharing is a multi-party cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed). When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bi-partite quantum key distribution (QKD) and those that exploit multi-partite entanglement. The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis t…
We present a scheme for key distribution based on bi-partite correlation of single photons. Alice keeps an ancilla photon and sends a signal photon to Bob, where intrinsic bi-partite correlation of these photons is obtained through first order intensity correlation in their detectors. The key bits are distributed through sharing four bi-partite correlation functions and photon counting. The scheme consists of two parts; first, Alice prepares deterministic photon states and Bob measures the photon states based on his random choice on correlation functions. Second, Alice guesses Bob's choice of …
The simulation of quantum correlations with alternative nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present the first known protocol that reproduces 3-partite GHZ correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the 3-partite GHZ state.
We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find…
We show that all multi-partite pure states can, under local operations, be transformed into bi-partite pairwise entangled states in a "lossless fashion": An arbitrary distinguished party will keep pairwise entanglement with all other parties after the asymptotic protocol - decorrelating all other parties from each other - in a way that the degree of entanglement of this party with respect to the rest will remain entirely unchanged. The set of possible entanglement distributions of bi-partite pairs is also classified. Finally, we point out several applications of this protocol as a useful primi…
Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multi-partite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for con…
Two pure states of a multi-partite system are alway are related by a unitary transformation acting on the Hilbert space of the whole system. This transformation involves multi-partite transformations. On the other hand some quantum information protocols such as the quantum teleportation and quantum dense coding are based on equivalence of some classes of states of bi-partite systems under the action of local (one-particle) unitary operations. In this paper we address the question: ``Under what conditions are the two states states, $\varrho$ and $σ$, of a multi-partite system locally unitary eq…
The squash operation, or the squashing model, is a useful mathematical tool for proving the security of quantum key distribution systems using practical (i.e., non-ideal) detectors. At the present, however, this method can only be applied to a limited class of detectors, such as the threshold detector of the Bennett-Brassard 1984 type. In this paper we generalize this method to include multi-partite measurements, such that it can be applied to a wider class of detectors. We demonstrate the effectiveness of this generalization by applying it to the device-independent security proof of the Ekert…
We show how to efficiently send an M-partite entangled state along a spin chain of arbitrary size. Specifically, we show how an entangled M-partite W sate can be almost flawlessly transmitted from one end (Alice) to the other end (Bob) of a spin-1/2 chain described by a slightly modified XX model. We achieve an almost perfect transmission without employing external magnetic fields or modulating the coupling constants among the spins of the chain, the two standard approaches used to achieve a good transmission efficiency. Moreover, the protocol here proposed can be used to transform an M-partit…
We introduce a family of QKD protocols for distributing shared random keys within a network of $n$ users. The advantage of these protocols is that any possible key structure needed within the network, including broadcast keys shared among subsets of users, can be implemented by using a particular multi-partite high-dimensional quantum state. This approach is more efficient in the number of quantum channel uses than conventional quantum key distribution using bipartite links. Additionally, multi-partite high-dimensional quantum states are becoming readily available in quantum photonic labs, mak…
We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In the entanglement swapping process, a four--partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot nois…
Entanglement is a powerful resource for processing quantum information. In this context pure, maximally entangled states have received considerable attention. In the case of bipartite qubit-systems the four orthonormal Bell-states are of this type. One of these Bell states, the singlet Bell-state, has the additional property of being antisymmetric with respect to particle exchange. In this contribution we discuss possible generalizations of this antisymmetric Bell-state to cases with more than two particles and with single-particle Hilbert spaces involving more than two dimensions. We review b…
We describe a protocol which can be used to generate any N-partite pure quantum state using Einstein-Podolsky-Rosen (EPR) pairs. This protocol employs only local operations and classical communication between the N parties (N-LOCC). In particular, we rely on quantum data compression and teleportation to create the desired state. This protocol can be used to obtain upper bounds for the bipartite entanglement of formation of an arbitrary N-partite pure state, in the asymptotic limit of many copies. We apply it to a few multipartite states of interest, showing that in some cases it is not optimal…
In this paper we show that sufficient multi-partite quantum entanglement helps in fair and unbiased election of a leader in a distributed network of processors with only linear classical communication complexity. We show that a total of $O(\log n)$ distinct multi-partite maximally entanglement sets (ebits) are capable of supporting such a protocol in the presence of nodes that may lie and thus be biased. Here, $n$ is the number of nodes in the network. We also demonstrate the difficulty of performing unbiased and fair election of a leader with linear classical communication complexity in the a…
We present an improved protocol for entanglement purification of bipartite mixed states using several states at a time rather than two at a time as in the traditional recurrence method. We also present a generalization of the hashing method to n-partite cat states, which achieves a finite yield of pure cat states for any desired fidelity. Our results are compared to previous protocols.
One notion of non-locality in quantum theory is the fact that information may be encoded in a composite system in such a way that it is not accessible through local measurements, even with the assistance of classical communication. Thus, contrary to the classical case, there exists information in quantum many body systems which cannot be accessed locally. We show however that, remarkably, two-dimensional subspaces do not have this property: any physically allowed measurement on information encoded in any two-dimensional subspace, regardless of entanglement or multi-partite structure, may be pe…
The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficien…
Intrinsic quantum correlations of weak coherent states are observed between two parties through a novel detection scheme, which can be used as a supplement to the existence decoy-state BB84 and differential phase-shift quantum key distribution (DPS-QKD) protocols. In a proof-of-principle experiment, we generate bi-partite correlations of weak coherent states using weak local oscillator fields in two spatially separated balanced homodyne detections. We employ nonlinearity of post-measurement method to obtain the bi-partite correlations from two single-field interferences at individual homodyne …
In this article we present a general security strategy for quantum secret sharing (QSS) protocols based on the HBB scheme presented by Hillery, Bužek and Berthiaume [Phys. Rev A \textbf{59}, 1829 (1999)]. We focus on a generalization of the HBB protocol to $n$ communication parties thus including $n$-partite GHZ states. We show that the multipartite version of the HBB scheme is insecure in certain settings and impractical when going to large $n$. To provide security for such QSS schemes in general we use the framework presented by some of the authors [M. Huber, F. Minert, A. Gabriel, B. C. Hie…
We present an explicit protocol ${\cal E}_0$ for faithfully teleporting an arbitrary two-qubit state via a genunie four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party GHZ and W states. We also give a dense coding scheme ${\cal D}_0$ involving our state as a shared resource of entanglement. Both ${\cal D}_0$ and ${\cal E}_0$ indicate that our four-qubit state is a likely candidate for the genunine four-partite analogue to a Bell state.
We consider the class of (N+1)-partite states suitable for protocols where there is a powerful party, the authority, and the other N parties play the same role, namely the state of their system live in the symmetric Hilbert space. We show that, within this scenario, there is a "maximally entangled state" that can be transform by a LOCC protocol into any other state. In addition, we show how to make the protocol efficiently including the construction of the state and discuss security issues for possible applications to cryptographic protocols. As an immediate consequence we recover a sequential…
Bellman's optimality principle has been of enormous importance in the development of whole branches of applied mathematics, computer science, optimal control theory, economics, decision making, and classical physics. Examples are numerous: dynamic programming, Markov chains, stochastic dynamics, calculus of variations, and the brachistochrone problem. Here we show that Bellman's optimality principle is violated in a teleportation problem on a quantum network. This implies that finding the optimal fidelity route for teleporting a quantum state between two distant nodes on a quantum network with…
Quantum mechanics allows operations to be in indefinite causal order. Recently there have been active discussions on enhanced communication strategies through exotic causal structures. In light of this, through the process matrix formalism, we formulate different classical capacities for a bi-partite quantum process. We find that a one-way communication protocol through an arbitrary process cannot outperform a causally separable process, i.e., we can send at most one bit per qubit. Next, we study bi-directional communication through a causally separable process. Our result shows, a bi-directio…
I show that W-like entangled quantum states are not a necessary quantum resource for totally correct anonymous leader election protocols. This is proven by defining a symmetric quantum state that is n-partite SLOCC inequivalent to the W state, and then constructing a totally correct anonymous leader election protocol using this state. This result, which contradicts the previous necessity result of D'Hondt and Panangaden, furthers our understanding of how non-local quantum states can be used as a resource for distributed computation.
We propose to produce five-partite entanglement via cascaded four-wave mixing in a high-Q microresonator that may become a key to future one-way quantum computation on chip. A theoretical model is presented for the underlying continuous-variable entanglement among the generated comb modes that is expansible to more complicated scenarios. We analyze the entanglement condition when the van Loock and Furusawa criteria are violated, and discuss the device parameters for potential experimental realization that may be utilized to build an integrated compact five-partite entanglement generator. The p…
The Goldenberg-Vaidman (GV) protocol for quantum key distribution (QKD) uses orthogonal encoding states of a particle. Its security arises because operations accessible to Eve are insufficient to distinguish the two states encoding the secret bit. We propose a two-particle cryptographic protocol for quantum secure direct communication, wherein orthogonal states encode the secret, and security arises from restricting Eve from accessing any two-particle operations. However, there is a non-trivial difference between the two cases. While the encoding states are perfectly indistinguishable in GV, t…
We present a multi-partite protocol in a counterfactual paradigm. In counterfactual quantum cryptography, secure information is transmitted between two spatially separated parties even when there is no physical travel of particles transferring the information between them. We propose here a tripartite counterfactual quantum protocol for the task of certificate authorization. Here a trusted third party, Alice, authenticates an entity Bob (e.g., a bank) that a client Charlie wishes to securely transact with. The protocol is counterfactual with respect to either Bob or Charlie. We prove its secur…
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett.…
Quantum correlations in observables of multiple systems not only are of fundamental interest, but also play a key role in quantum information processing. As a signature of these correlations, the violation of Bell inequalities has not been demonstrated with multipartite hybrid entanglement involving both continuous and discrete variables. Here we create a five-partite entangled state with three superconducting transmon qubits and two photonic qubits, each encoded in the mesoscopic field of a microwave cavity. We reveal the quantum correlations among these distinct elements by joint Wigner tomo…
For a tripartite pure state of three qubits, it is well known that there are two inequivalent classes of genuine tripartite entanglement, namely the GHZ-class and the W-class. Any two states within the same class can be transformed into each other with stochastic local operations and classical communication (SLOCC) with a non-zero probability. The optimal conversion probability, however, is only known for special cases. Here, we derive new lower and upper bounds for the optimal probability of transformation from a GHZ-state to other states of the GHZ-class. A key idea in the derivation of the …
A new scheme of Quantum Key Distribution is proposed using three entangled particles in a GHZ state. Alice holds a 3-particle source and sends two particles to Bob, keeping one with herself. Bob uses one particle to generate a secure key, and the other to generate a master-key. This scheme should prove to be harder to break in non-ideal situations as compared to the standard protocols BB84 and Eckert. The scheme uses the concept of Quantum Disentanglement Eraser. Extension to multi-partite scheme has also been investigated.
We present a practical entanglement distillation protocol (EDP) with linear optics for a genuine mixed state. Each components of the genuine mixed state is a pure less-entangled state. After successfully performing this EDP, we can obtain a high quality entangled mixed state. Our EDP can work for both ideal entanglement sources and current available spontaneous parametric down-conversion (SPDC) sources, which makes it feasible in current experimental technology. Moreover, by using the SPDC source, we can obtain a higher fidelity. This protocol can also be used to distill the multi-partite enta…
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.
Quantum state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multi-partite quantum networks. Quantum state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret state distribution, and a class of "quantum disentangling" protocols for the state reconstruction. We demonstrate a quantum state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to…
Recently, a quantum multi-party summation protocol based on the quantum Fourier transform has been proposed [Quantum Inf Process 17: 129, 2018]. The protocol claims to be secure against both outside and participant attacks. However, a closer look reveals that the player in charge of generating the required multi-partite entangled states can launch two kinds of attacks to learn about other parties' private integer strings without being caught. In this paper, we present these attacks, and propose countermeasures to make the protocol secure again. The improved protocol not only can resist these a…
The communication cost of simulating probability distributions obtained by measuring quantum states is a natural way to quantify quantum non-locality. While much is known in the case of bipartite entanglement, little has been done in the multipartite setting. In this paper, we focus on the GHZ state. Specifically, equatorial measurements lead to correlations similar to the ones obtained with Bell states. We give a protocol to simulate these measurements on the n-partite GHZ state using O(n^2) bits of communication on average.
We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is tra…
