Multi-qubit Entangled States Research Articles

Unified Monogamy Relations of Multipartite Entanglement

Unified-(q, s) entanglement ({{mathscr{U}}}_{q,s}) is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of {{mathscr{U}}}_{q,s}. Then, the monogamy relation based on the squared {{mathscr{U}}}_{q,s} for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power {{mathscr{U}}}_{q,s} based general monogamy and polygamy inequalities are established for tripartite qubit states.

Entanglement in a 20-Qubit Superconducting Quantum Computer

The ability to prepare sizeable multi-qubit entangled states with full qubit control is a critical milestone for physical platforms upon which quantum computers are built. We investigate the extent to which entanglement is found within a prepared graph state on the 20-qubit superconducting quantum computer IBM Q Poughkeepsie. We prepared a graph state along a path consisting of all twenty qubits within the device and performed full quantum state tomography on all groups of four connected qubits along this path. We determined that each pair of connected qubits was inseparable and hence the prepared state was entangled. Additionally, a genuine multipartite entanglement witness was measured on all qubit subpaths of the graph state and we found genuine multipartite entanglement on chains of up to three qubits. These results represent a demonstration of entanglement in one of the largest solid-state qubit arrays to date and indicate the positive direction of progress towards the goal of implementing complex quantum algorithms relying on such effects.

Quantum e-commerce: a comparative study of possible protocols for online shopping and other tasks related to e-commerce

A set of quantum protocols for online shopping is proposed and analyzed to establish that it is possible to perform secure online shopping using different types of quantum resources. Specifically, a single photon based, a Bell state based and two 3-qubit entangled state based quantum online shopping schemes are proposed. The Bell state based scheme, being a completely orthogonal state based protocol, is fundamentally different from the earlier proposed schemes which were based on conjugate coding. One of the 3-qubit entangled state based scheme is build on the principle of entanglement swapping which enables us to accomplish the task without transmission of the message encoded qubits through the channel. Possible ways of generalizing the entangled state based schemes proposed here to the schemes which use multiqubit entangled states is also discussed. Further, all the proposed protocols are shown to be free from the limitations of the recently proposed protocol of Huang et al. (Quantum Inf. Process. 14, 2211-2225, 2015) which allows the buyer (Alice) to change her order at a later time (after initially placing the order and getting it authenticated by the controller). The proposed schemes are also compared with the existing schemes using qubit efficiency.

Cyclic and Bidirectional Quantum Teleportation via Pseudo Multi-Qubit States

A novel scheme is proposed in this paper, which realizes the cyclic and bidirectional teleportation via pseudo multi-qubit entangled states. To realize the teleportation completely, it utilizes controlled-NOT operation to obtain a quantum channel whose number of qubits reaches twelve. In this scheme, Alice can teleport her qubits to Bob and Charlie, Bob can teleport his qubits to Alice and Charlie while Charlie teleports his qubits to Alice and Bob, respectively, they reconstruct the original state and make the scheme perfectly by performing Bell-state measurement and appropriate unitary operation.

Generation and swapping of multi-qubit entangled state in a coupled superconducting resonator array

An efficient method is proposed for the generation and swapping of multi-qubit entangled state in an array of linearly coupled superconducting resonators, each of which is coupled to N superconducting qubits. With the external driving fields to adjust the desired qubit–resonator interaction, we firstly show that the multipartite entangled state of superconducting qubits hosted in two nearest-neighbor interacting resonators can be deterministically realized. Furthermore, by utilizing the produced entangled state, we put forward a protocol for the swapping of quantum entangled state in the coupled resonator array based on measurement, i.e., the multi-particle entangled state can be achieved for the qubits in long-distance separated resonators. The numerical simulation suggests that our scheme is feasible with current circuit QED technology.

Analysing nonlocality robustness in multiqubit systems under noisy conditions and weak measurements

We analyse robustness of nonlocal correlation in multiqubit entangled states—three- and four-qubit GHZ class and three-qubit W class—useful for quantum information and computation, under noisy conditions and weak measurements. For this, we use a Bell-type inequality whose violation is considered as a signature for confirming the presence of genuine nonlocal correlations between the qubits. In order to demonstrate the effects of noise and weak measurements, an analytical relation is established between the maximum expectation value of three and four-qubit Svetlichny operators for the systems under study, noise parameter and strengths of weak measurements. Our results show that for a set of three- and four-qubit GHZ class states, maximal nonlocality does not coincide with maximum entanglement for a given noise parameter and a certain range of weak measurement parameter. Our analysis further shows an excellent agreement between the analytical and numerical results.

Multiqubit UPB: the method of formally orthogonal matrices

We use formal matrices whose entries we view as vector variables taking unit vector values in one-qubit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and provide a new construction of UPBs of n qubits of cardinality n + 1 when . We also give a new method of constructing multiqubit entangled states with all partial transposes positive.

Schemes for Hybrid Bidirectional Controlled Quantum Communication via Multi-qubit Entangled States

We present two schemes for hybrid bidirectional controlled quantum communication (HBCQC) via six- and nine-qubit entangled states as the quantum channel, respectively. In these schemes, two distant parties, Alice and Bob are not only senders but also receivers, and Alice wants to teleport an unknown single-qubit state to Bob, at the same time, Bob wishes to help Alice remotely prepares an arbitrary single- and two- qubit state, respectively. It is shown that, only if the two senders and the controller collaborate with each other, the HBCQC can be completed successfully. We demonstrate, in our both schemes, the total success probability of the HBCQC can reach 1, that is, the schemes are deterministic.

Almost all multipartite qubit quantum states have trivial stabilizer

The stabilizer group of an n-qubit state |ψ is the set of all matrices of the form g=g1⊗⋯⊗gn, with g1,…,gn being any 2 × 2 invertible complex matrices that satisfy g|ψ=|ψ. We show that for 5 or more qubits, except for a set of states of zero measure, the stabilizer group of multipartite entangled states is trivial, that is, containing only the identity element. We use this result to show that for 5 or more qubits, the action of deterministic local operations and classical communication (LOCC) can almost always be simulated simply by local unitary (LU) operations. This proves that almost all n-qubit states with n≥5 can neither be reached nor be converted into any other (n-partite entangled), LU-inequivalent state via deterministic LOCC. We also find a simple and elegant expression for the maximal probability to convert one multi-qubit entangled state to another for this generic set of states.

Blind Quantum Signature with Controlled Four-Particle Cluster States

A novel blind quantum signature scheme based on cluster states is introduced. Cluster states are a type of multi-qubit entangled states and it is more immune to decoherence than other entangled states. The controlled four-particle cluster states are created by acting controlled-Z gate on particles of four-particle cluster states. The presented scheme utilizes the above entangled states and simplifies the measurement basis to generate and verify the signature. Security analysis demonstrates that the scheme is unconditional secure. It can be employed to E-commerce systems in quantum scenario.

Experimental characterization of a non-local convertor for quantum photonic networks.

We experimentally characterize a quantum photonic gate that is capable of converting multiqubit entangled states while acting only on two qubits. It is an important tool in large quantum networks, where it can be used for re-wiring of multipartite entangled states or for generating various entangled states required for specific tasks. The gate can be also used to generate quantum information processing resources, such as entanglement and discord. In our experimental demonstration, we characterized the conversion of a linear four-qubit cluster state into different entangled states, including GHZ and Dicke states. The high quality of the experimental results show that the gate has the potential of being a flexible component in distributed quantum photonic networks.

Blind Quantum Signature with Blind Quantum Computation

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client’s privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

A Criterion for Maximally Six-Qubit Entangled States via Coefficient Matrix

In a recent paper (J. Phys. A: Math. Theor 45, 075308 (2012)), Li et al. established the coefficient matrix of six-qubit entangled states. With an emphasis on six qubits, we present a new criterion for maximally six-qubit entangled states via those coefficient matrices. By calculating the determinants of coefficient matrix, one use the criterion that characterize these states. Moreover, the criterion via the coefficient matrices gives rise to the combination of maximally multi-qubit entangled state(MMES) and matrix, and we believe that the new criterion can play an important role in quantum information.

Dissipation-assisted quantum correlations in coupled qubits

We theoretically investigate a possibility to establish multi-qubit quantum correlations in one-dimensional chains of qubits. We combine a reservoir engineering strategy with coherent dynamics to generate multi-qubit entangled states. We find that an interplay between the coherent and incoherent dynamics result in the generation of stable (time-independent) many-body entangled steady states. Our results will be relevant in the context of the dissipative generation of quantum states, with applications in short-distance quantum computation and for exploring the emergence of collective phenomena in many-body open quantum systems.

General monogamy of Tsallisq-entropy entanglement in multiqubit systems

In this paper, we study the monogamy inequality of Tsallis-q entropy entanglement. We first provide an analytic formula of Tsallis-q entropy entanglement in two-qubit systems for $\frac{5-\sqrt{13}}{2}\leq q\leq\frac{5+\sqrt{13}}{2}.$ The analytic formula of Tsallis-q entropy entanglement in $2\otimes d$ system is also obtained and we show that Tsallis-q entropy entanglement satisfies a set of hierarchical monogamy equalities. Furthermore, we prove the squared Tsallis-q entropy entanglement follows a general inequality in the qubit systems. Based on the monogamy relations, a set of multipartite entanglement indicators is constructed, which can detect all genuine multiqubit entangled states even in the case of $N$-tangle vanishes. Moreover, we study some examples in multipartite higher-dimensional system for the monogamy inequalities.

Pretty good state transfer of entangled states through quantum spin chains

The XX model with uniform couplings represents the most natural choice for quantum state transfer through spin chains. Given that it has long been established that single-qubit states cannot be transferred with perfect fidelity in this model, the notion of pretty good state transfer has been recently introduced as a relaxation of the constraints on fidelity. In this paper, we study the transfer of multi-qubit entangled and unentangled states through unmodulated spin chains, and we prove that it is possible to have pretty good state transfer of any multi-particle state. This significantly generalizes the previous results on single-qubit state transfer and opens the way to using uniformly coupled spin chains as short-distance quantum channels for the transfer of arbitrary states of any dimension. Our results could be tested with current technology.

General monogamy relation for the entanglement of formation in multiqubit systems.

We prove exactly that the squared entanglement of formation, which quantifies the bipartite entanglement, obeys a general monogamy inequality in an arbitrary multiqubit mixed state. Based on this kind of exotic monogamy relation, we are able to construct two sets of useful entanglement indicators: the first one can detect all genuine multiqubit entangled states even in the case of the two-qubit concurrence and n-tangles being zero, while the second one can be calculated via quantum discord and applied to multipartite entanglement dynamics. Moreover, we give a computable and nontrivial lower bound for multiqubit entanglement of formation.

Spin Ensembles Coupled to Superconducting Resonators: A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.

Perfect state transfer and efficient quantum routing: A discrete-time quantum-walk approach

We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

Electrically Controlled Eight‐Spin‐Qubit Entangled‐State Generation in a Molecular Break Junction

The generation of spin-based multi-qubit entangled states in the presence of an electric field is one of the most challenging tasks in current quantum-computing research. Such examples are still elusive. By using non-equilibrium Green's function-based quantum-transport calculations in combination with non-collinear spin density functional theory, we report that an eight-spin-qubit entangled state can be generated with the high-spin state of a dinuclear Fe(II) complex when the system is placed in a molecular break junction. The possible gate operation scheme, gating time, and decoherence issues have been carefully addressed. Furthermore, our calculations reveal that the preservation of the high spin state of this complex is possible if the experimentalists keep the electric-field strength below 0.78 V nm(-1). In brief, the present study offers a unique way to realize the first example of a multi-qubit entangled state by electrical means only.