Four-qubit States Research Articles

Two Forms Schemes of Deterministic Remote State Preparation for Four-Qubit Cluster-Type State

Two deterministic schemes are put forward to preparing an arbitrary four-qubit cluster-type state remotely by using two Bell states as quantum channel. The coefficients of the prepared states can be not only real, but also complex. To accomplish the schemes, we introduce some novel sets of ingenious measurement basis vectors. Especially, for complex coefficients case, we give two different forms schemes. The receiver will reconstruct the initial state by means of some appropriate unitary operations. The outstanding advantage of the present schemes is that the success probability in all the considered remote state preparation (RSP) can reach 1.

Noise tolerance of Dicke states

Starting from explicitly constructing an entanglement witness for the mixture of a Dicke state with white noise (noisy Dicke state), we provide an entanglement criterion for any multiqubit state. The criterion is necessary and sufficient for noisy $W$ states of three, four, and five qubits. We demonstrate an entanglement criterion for any four-qubit state. The criterion is necessary and sufficient for the generalized noisy four-qubit Dicke states. We present the sufficient criterion of full separability for a noisy $2k$ qubit Dicke state with $k$ excitations. Then we generalize the entanglement witness and criterion to the mixture of white noise and generic $n$-qubit Dicke state with $k$ excitations based on strong numeric evidence. Apart from noisy Dicke states, we also consider the entanglement properties of simultaneously amplitude damped and dephased Dicke states, and depolarized multiqubit $W$ states.

Bidirectional Quantum Teleportation by Using a Four-Qubit GHZ State and Two Bell States

In this paper, a theoretical scheme for bidirectional quantum teleportation by using a four-qubit GHZ state and two Bell states as a quantum channel is proposed. In this scheme, two arbitrary single-qubit quantum states and an unknown three-qubit state can be mutually transmitted between the two communication participants Alice and Bob. The quantum state information can be transmitted if Alice performs four single-qubit measurement operations on her qubits and Bob carries out a four-qubit joint measurement on his qubits, respectively. Then both Alice and Bob can reconstruct the target quantum state by means of appropriate unitary operations. Then we take comparisons with the other bidirectional quantum teleportation protocols in five aspects of quantum information bits transmitted, necessary operations, consumption of quantum resource, consumption of classical resource and intrinsic efficiency. Furthermore, we use channel authentication method to ensure the channel security and prove that our protocol can withstand four attack scenarios. It is concluded that our scheme has significant advantages of more qubits number transmitted, higher intrinsic efficiency and high security.

Enhanced Multiqubit Phase Estimation in Noisy Environments by Local Encoding.

The first generation of multiqubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error protection that meets a careful trade-off between noise protection and resource overhead. Here, we experimentally demonstrate that single-qubit encoding can significantly enhance the robustness of entanglement and coherence of four-qubit graph states against local noise with a preferred direction. In particular, we explicitly show that local encoding provides a significant practical advantage for phase estimation in noisy environments. This demonstrates the efficacy of local unitary encoding under realistic conditions, with potential applications in multiqubit quantum technologies for metrology, multipartite secrecy, and error correction.

Deterministic Secure Four-qubit GHZ States Three-step Protocol for Quantum Communication

A deterministic secret quantum communication (DSQC) protocol is proposed with four-qubit GHZ states. It has some outstanding advantages. Firstly, it has a high communication capacity as each four-qubit GHZ state can carry three bits of secret messages. Secondly, as all of the quantum resource is useful, the intrinsic efficiency of the communication approaches the maximum value 100%. Besides, its total efficiency of the present protocol is 60%, more higher than most of the current existing DSQC protocols. The decoy photon detection technique guarantees that Eve’s any eavesdropping behavior can be detected on site, and the three-step transmitting strategy ensures no information will be leaked in the communication process. Moreover, the present protocol is feasible with the present day technique.

A universal protocol for controlled bidirectional quantum state transmission

In this paper, we propose a universal protocol for controlled bidirectional quantum state transmission. The bidirectional transmission of $$ n_{1} $$ - and $$ n_{2} $$ -qubit equatorial states can be realized by using the $$ 2n_{1} + 2n_{2} + 1 $$ -qubit entangled state as the quantum channel, where $$ n_{1} ,n_{2} $$ are arbitrary nonzero positive integers. First, the quantum channel is constructed by using Hadamard (H) and CNOT operations. Furthermore, after the protocol completed, the desired state can be obtained simultaneously, securely and determinately. Second, two examples are given. One is a symmetric protocol which can complete the bidirectional transmission of two-qubit equatorial state. The other is an asymmetric protocol, where Alice transmits a single-qubit equatorial state to Bob and Bob transmits a four-qubit equatorial state to Alice. To the best of our knowledge, it is the first time to realize the bidirectional transmission of arbitrary-qubit equatorial state. At last, we analyze the performance of the protocol. Some comparisons with other protocols are described.

Analyzing the entanglement properties of graph states with generalized concurrence

We propose a new classification for the entanglement in graph states based on generalized concurrence. The numerical results indicate that the eight different three-qubit graph states in three categories, 64 four-qubit graph states in five categories and 1024 five-qubit graph states in 10 classes. We also compare this classification with equivalence classes of these graph states under local complementation (LC) operator, and the obtained result suggests that classification by generalized concurrence is not in contradiction with the LC-rule. Furthermore, our results suggest that the generalized concurrence is a suitable measure of entanglement for multi-qubit graph states.

An optional remote state preparation protocol for a four-qubit entangled state

In this paper, we introduce a remote state preparation protocol for the case of a known four-qubit entangled state in which there are two possible receivers and the sender has the option of choosing one of the two possible parties for a preparation of the intended state at the end of the chosen party. The sender begins with a measurement on a two-qubit system in which the measurement basis is chosen by using the known information of the state. After that she exercises her option which is exclusively her own prerogative. The protocol has four components depending on the four different measurement results of the sender. The scheme is compared in terms of efficiency with other contemporary remote state preparation protocols for similar purposes.

Remote preparation of four-qubit states via two-qubit maximally entangled states

In this paper, an efficient scheme of remotely preparing four-qubit quantum states via two-qubit maximally entangled states is proposed. This scheme can be accomplished by using appropriate unitary transformations and some classical communication. The detailed processes for preparation of four-qubit states are presented in the general case and two special cases, respectively. The method of constructing special measurement basis in general case is provided, and the similar methods for real-parameter state case and equatorial state case are also discussed. Meanwhile, the probabilities of successful preparation under each case are calculated in our schemes. The results show that the successful probability is only 1 / 16 in the general case, and the probability can reach up to 100% when the relative phase factors are zero or the amplitude parameters are 1 / 4.

Verifiable Quantum Secret Sharing Protocols Based on Four-Qubit Entangled States

A new verifiable three-party quantum secret sharing protocol is proposed based on a special four-qubit entangled state which is inequivalent to four-qubit singlet states under stochastic local operations and classical communication (SLOCC). The validity of the reconstructed secret is verifiable based on the method like Byzantine agreement. It is generalized to verifiable multiparty quantum secret sharing based on four-qubit entangled states. It is shown to be secure against common attacks and feasible with present-day technology. PACS number(s): 03.67.Dd, 03.67.Hk, 03.67.Lx.

Precise detection of multipartite entanglement in four-qubit Greenberger–Horne–Zeilinger diagonal states

We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger--Horne--Zeilinger (GHZ) diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.

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.

Effects of Lorentz boosts on Dirac bispinor entanglement

In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity-spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking diffrences between the appropriate approach for this case and the one usually treated in the literature are discussed.

Deterministic Secure Quantum Communication with Four-qubit GHZ States

Based on the order rearrangement strategy, a deterministic secure quantum communication (DSQC) scheme by utilizing the four-qubit GHZ states as quantum channel is proposed. The intrinsic efficiency for qubits of the present scheme reaches the maximal value 100%. In order to improve its total efficiency of communication, the security protect measures of the present scheme can be modified following with the two-step transmitting idea, and the total efficiency of the revised scheme can come up to 40%, more higher than some previous DSQC schemes. Finally, some issues for the practical application of our schemes are discussed.

On monogamy of four-qubit entanglement

Our main result is a monogamy inequality satisfied by the entanglement of a focus qubit (one-tangle) in a four-qubit pure state and entanglement of subsystems. Analytical relations between three-tangles of three-qubit marginal states, two-tangles of two-qubit marginal states and unitary invariants of four-qubit pure state are used to obtain the inequality. The contribution of three-tangle to one-tangle is found to be half of that suggested by a simple extension of entanglement monogamy relation for three qubits. On the other hand, an additional contribution due to a two-qubit invariant which is a function of three-way correlations is found. We also show that four-qubit monogamy inequality conjecture of ref. [PRL 113, 110501 (2014)] in which three-tangles are raised to the power (3/2), does not estimate the residual correlations, correctly. A lower bound on residual four-qubit correlations is obtained.

Optimal nonlocal conversion of photonic four-partite entanglement from two Bell pairs in quantum networks

We analyze optimal schemes and also propose some practical schemes for the nonlocal conversion from two shared Bell pairs to four-qubit entangled states in optical quantum networks. In the analysis, we consider two-qubit operations as nonlocal operations and minimize the number of access to ancillary qubits as possible. First, we consider two-qubit unitary operations without using ancillary qubits and derive a necessary and sufficient condition for convertible states. Second, we consider nonlocal optical systems composed of passive linear optics and postselection. For the passive linear optical systems, we derive achievable upper bounds of success probabilities of the conversion in the case without ancillary qubits. We also compare the optimal success probabilities with those of previously proposed schemes. Finally, we discuss success probabilities of the conversion in the case with ancillary qubits.

Deterministic quantum dense coding networks

We consider the scenario of deterministic classical information transmission between multiple senders and a single receiver, when they a priori share a multipartite quantum state – an attempt towards building a deterministic dense coding network. Specifically, we prove that in the case of two or three senders and a single receiver, generalized Greenberger–Horne–Zeilinger (gGHZ) states are not beneficial for sending classical information deterministically beyond the classical limit, except when the shared state is the GHZ state itself. On the other hand, three- and four-qubit generalized W (gW) states with specific parameters as well as the four-qubit Dicke states can provide a quantum advantage of sending the information in deterministic dense coding. Interestingly however, numerical simulations in the three-qubit scenario reveal that the percentage of states from the GHZ-class that are deterministic dense codeable is higher than that of states from the W-class.

A multi-hop teleportation protocol of arbitrary four-qubit states through intermediate nodes

Teleportation processes over long distances become affected by the almost inevitable existence of noise which interferes with the entangled quantum channels. In view of this, intermediate nodes are introduced in the scheme. These nodes are connected in series through quantum entanglement. In this paper, we present a protocol for transferring an entangled four-particle cluster-type state in an integrated manner through the intermediate nodes. Its efficiency and advantage over the corresponding part by part teleportation process is discussed.

Four-qubit systems and dyonic black Hole–Black branes in superstring theory

Using dyonic solutions in the type IIA superstring theory on Calabi–Yau (CY) manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BHs) and black 2-branes (B2B) carrying eight electric charges and eight magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on [Formula: see text] to four-qubit states. These states are interpreted in terms of such dyonic charges resulting from the quaternionic symmetric space [Formula: see text] corresponding to a [Formula: see text] sigma model superpotential in two dimensions. The superpotential is considered as a functional depending on four quaternionic fields mapped to a class of Clifford algebras denoted as [Formula: see text]. A link between such an algebra and the cohomology classes of [Formula: see text] in heterotic superstring theory is also given.

A new method for constructing entangled states via orthogonal arrays

A pure quantum state of $N$ subsystems with $d$ levels each is called $k$-multipartite maximally entangled state, which we call a $k$-uniform state, if all its reductions to $k$ qubits are maximally mixed. Recently, Goyeneche and Zyczkowski proposed a method of constructing $k$-uniform states via orthogonal arrays, by which, we will also propose a new method to construct quantum states with orthogonal arrays in this paper, which is the method of increasing phase parameters. We can find the quantum states constructed via our new method by using the same orthogonal array, for four-qubit quantum states, not only are they 1-uniform states, also may become maximally entangled states; for five-qubit quantum states, we find that it can make the original 1-uniform states into 2-uniform states. In particular, for four-qubit quantum states, we can construct a series of new forms of maximally entangled states via our new method.