Multiqubit Entanglement Research Articles

Special entangled quantum systems and the Freudenthal construction

We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant under the group of stochastic local operations and classical communication (SLOCC). For this type of multipartite entanglement the SLOCC classes can be explicitly given. These results enable further explicit constructions of multiqubit entanglement measures for distinguishable constituents by embedding them into identical fermionic ones. We also prove that the Plücker relations for the embedding system provide a sufficient and necessary condition for the separability of the embedded one. We argue that this embedding procedure can be regarded as a convenient representation for quantum systems of particles which are really indistinguishable but for some reason they are not in the same state of some inner degree of freedom.

PERFECT TELEPORTATION OF UNKNOWN QUDIT BY A d-LEVEL GHZ CHANNEL

In the past decades, various schemes of teleportation of quantum states through different types of quantum channels (a prior shared entangled state between the sender and the receiver), e.g. EPR pairs, generalized Bell states, qubit GHZ states, standard W states and its variations, genuine multiqubit entanglement states, etc., have been developed. Recently, three-qutrit quantum states and two-qudit quantum states have also been considered as quantum channels for teleportation. In this paper, we investigate the teleportation of an unknown qudit using a d level GHZ state, i.e. a three-qudit maximally entangled state, as quantum channel. We design a general scheme of faithful teleportation of an unknown qudit using a d-level GHZ state shared between the sender and the receiver, or among the sender, the receiver and the controller; an unknown two-qudit of Schmidt form using a d level GHZ state shared between the sender and the receiver; as well as an unknown arbitrary two-qudit using two shared d level GHZ states between the sender, the receiver and the controller, or using one shared d level GHZ state and one shared generalized Bell state. We obtain the general formulas of Alice's measurement basis, Charlie's measurement basis and Bob's unitary operations to recover the input state of Alice. It is intuitionistic to generalize the protocols of teleporting an arbitrary two-qudit state to teleporting an arbitrary n-qudit state.

ENTANGLEMENT VERSUS ENERGY IN MULTIQUBIT ENTANGLEMENT DYNAMICS PROBLEM

We study the relation between energy and entanglement in a multiqubit entanglement dynamics problem in cavity QED. The model consists of three two-level atoms A, B and C which are initially prepared in a Greenberger–Horne–Zeilinger-like state and locally coupled with independent cavities a, b and c, respectively. We shall show that the dynamical evolution of atomic entanglement is closely related to that of their energy.

Scheme for realizing quantum computation and quantum information transfer with superconducting qubits coupling to a 1D transmission line resonator

This paper proposes a simple scheme for realizing one-qubit and two-qubit quantum gates as well as multiqubit entanglement based on dc-SQUID charge qubits through the control of their coupling to a 1D transmission line resonator (TLR). The TLR behaves effectively as a quantum data-bus mode of a harmonic oscillator, which has several practical advantages including strong coupling strength, reproducibility, immunity to 1/f noise, and suppressed spontaneous emission. In this protocol, the data-bus does not need to stay adiabatically in its ground state, which results in not only fast quantum operation, but also high-fidelity quantum information processing. Also, it elaborates the transfer process with the 1D transmission line.

Multiqubit entanglement engineering via projective measurements

We present strategies to obtain different classes of three and four photon entangled symmetric states from a single experimental setup. The basic idea originates from the property of the symmetric Dicke state with two excitations to connect the two inequivalent types of genuine tripartite entanglement. We experimentally confirm the distinct types of entanglement of the observed states. We further propose an extension of the applied scheme that allows one to obtain different classes of four-photon entanglement by adding a fifth photon. The requirement of a single fifth photon is currently a technical challenge, and thus we consider the approach of using a strongly attenuated weak coherent beam instead.

Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic Greenberger-Horne-Zeilinger and W states. In the case of three emitters, where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between well-defined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.

Preparation of a New Type of Multiqubit Entangled States in Cavity QED

Recently Yang, Chu, and Han [Phys. Rev. A 70 (2004) 022329] presented a new type of multipartite entangled states for implementing efficient many-party controlled teleportation of multiqubit quantum information. Here we propose a simple scheme for preparing such a type of multi-atom entangled states in cavity quantum electrodynamics (QED). The scheme involves atom-cavity interaction with large detuning, and is immune to the cavity decay and the thermal field states. Some practical analyses show its availability with the present technology.

Partial separability and entanglement criteria for multiqubit quantum states

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-\ifmmode \dot{Z}\else \.{Z}\fi{}ukowski criterion, and the D\"ur-Cirac criterion) and also by showing their great noise robustness for a variety of multiqubit states, including $N$-qubit Greenberger-Horne-Zeilinger states and Dicke states. Furthermore, for $N\ensuremath{\geqslant}3$ they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only $N+1$. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the antidiagonal matrix elements of a state in terms of its diagonal matrix elements.

Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment

We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of the complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between either of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger type.

SOME ENTANGLEMENT FEATURES OF HIGHLY ENTANGLED MULTIQUBIT STATES

We explore some basic entanglement features of multiqubit systems that are relevant for the development of algorithms for searching highly entangled states. In particular, we compare the behaviours of multiqubit entanglement measures based (i) on the von Neumann entropy of marginal density matrices and (ii) on the linear entropy of those matrices.

ENTANGLEMENT DISTRIBUTION AND STATE DISCRIMINATION IN TRIPARTITE QUBIT SYSTEMS

This work reviews and extends recent results concerning the distribution of entanglement, as well as nonlocality (in terms of inequality violations) in tripartite qubit systems. With recourse to a Monte Carlo generation of pure and mixed states of three-qubits, we explore several features related to the distribution of entanglement (expressed in the form of different measures of multiqubit entanglement based upon bipartitions). Also, special interest is paid to maximally entangled states (such as the GHZ for three-qubits) and W states. This study also sheds some light on the interesting relation existing between some entanglement measures and perfect state discrimination in LOCC measurements relevant to cryptographic protocols. We round off the results by studying the distribution of entanglement between Alice and Bob in a modified teleportation protocol toy model over three-qubit states.

Multi-qubit stabilizer and cluster entanglement witnesses

One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed by using the stabilizer operators of some given multi-qubit states such as GHZ, cluster and exceptional states. The general approach to manipulate the multi-qubit stabilizer EWs by exact(approximate) linear programming (LP) method is described and it is shown that the Clifford group play a crucial role in finding the hyper-planes encircling the feasible region. The optimality, decomposability and non-decomposability of constructed stabilizer EWs are discussed.

Nonlinear Response and Observable Signatures of Equilibrium Entanglement

We investigate how equilibrium entanglement is manifested in the nonlinear response of an N-qubit system. We show that in the thermodynamic limit the irreducible part of the nth-order nonlinear susceptibility indicates that the eigenstates of the system contain entangled (n + 1)-qubit clusters. This opens the way to a directly observable multiqubit entanglement signature. We show that the irreducible part of the static cubic susceptibility of a system of four flux qubits, as a function of external parameters, behaves as a global 4-qubit entanglement measure introduced in Ref. (20). We discuss the possibility of extracting purely-entanglement-generated contribution from the general multipoint correlators in a multiqubit system.

The geometry of multi-qubit entanglement

This paper, a continuation of a previous one (Iwai 2007 J. Phys. A: Math. Theor. 40 1361), studies the geometry of multi-qubit entanglement with respect to bipartite partitions. An n-qubit system (C2)⊗n is isomorphic with , the linear space of 2ℓ × 2m complex matrices, where ℓ + m = n. According to the isomorphism, the local transformation group U(2ℓ) × U(2m) acts on the space of normalized states in . Let M and G denote the space of normalized states and the local transformation group acting on M, respectively. According to the orbit types, M is stratified into strata, among which a principal stratum and the sets of separable states and maximally entangled states will be identified. For , a function F(C) = det(I − CC*) proves to serve as a measure of entanglement, where I denotes the 2ℓ × 2ℓ identity matrix. The F(C) attains the minimal and the maximal values, respectively, on the sets of separable states and maximally entangled states, and further takes no extremal values on the principal stratum. The F(C) projects to a function on the factor space G\\M. A naturally defined metric on M also projects to that on G\\M, which serves to measure the distance between the separable states, F−1(0), and the states, F−1(k), of prescribed value k of measure. To be precise, one has to restrict M to the principal stratum, when projecting the metric. Three- and four-qubit systems will be studied intensively, and then multi-qubit systems discussed.

Multiqubit entanglement witness

We introduce a feasible method of constructing the entanglement witness that detects genuine multiqubit entanglement in the vicinity of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are most often investigated theoretically and experimentally. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.

Genuine multiqubit entanglement and controlled teleportation

We construct a genuine $(2N+1)$-qubit entangled state to perform controlled teleportation of an arbitrary $N$-qubit state. The constructed state is a complementarity to the genuine $2N$-qubit entangled state constructed by Yeo and Chua for $N=2$ [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen, Zhu, and Guo for any $N$ [Phys. Rev. A 74, 032324 (2006)]. We also quantify the entanglement of the state and classify it with the well-known $GHZ$ and $W$ states by means of the recently proposed generalized global entanglement and the associated auxiliary measures [Phys. Rev. A 74, 022314 (2006)]. Our study is of general importance with respect to exploring and exploiting the genuine multiqubit entanglement.

Entangling spins by measuring charge: A parity-gate toolbox

The parity gate emerged recently as a promising resource for performing universal quantum computation with fermions using only linear interactions. Here we analyze the parity gate ($P$ gate) from a theoretical point of view in the context of quantum networks. We present several schemes for entanglement generation with $P$ gates and show that native networks simplify considerably the resources required for producing multiqubit entanglement, such as $n$--Greenberg-Horne-Zellinger (GHZ) states. Other applications include a Bell-state analyzer and teleportation. We also show that cluster state fusion can be performed deterministically with parity measurements. We then extend this analysis to hybrid quantum networks containing spin and mode qubits. Starting from an easy-to-prepare resource (spin-mode entanglement of single electrons) we show how to produce a spin $n$-GHZ state with linear elements (beam splitters and local spin flips) and charge-parity detectors; this state can be used as a resource in a spin quantum computer or as a precursor for constructing cluster states. Finally, we construct an alternative spin-controlled-$Z$ gate by using the mode degrees of freedom as ancill\ae{}.

Tavis-Cummings model and collective multiqubit entanglement in trapped ions

We present a method of generating collective multi-qubit entanglement via global addressing of an ion chain following the guidelines of the Tavis-Cummings model, where several qubits are coupled to a collective motional mode. We show that a wide family of Dicke states and irradiant states can be generated by single global laser pulses, unitarily or helped with suitable postselection techniques.

Characterization of multiqubit pure-state entanglement

A necessary and sufficient entanglement criterion based on variances of Mermin-Klyshko's Bell operators is proved for multiqubit pure states. Contrary to Bell's inequalities, entangled pure states strictly satisfy a quadratic inequality but product ones can attain the equality under some local unitary transformations, which can be obtained by solving a quadratic maximum problem. This presents a characterization of multiqubit pure-state entanglement.

Geometric Quantum Computation and Multiqubit Entanglement with Superconducting Qubits inside a Cavity

We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the cavity. We illustrate how to physically implement universal quantum computation as well as multiqubit entanglement based on unconventional geometric phase shifts in this scalable solid-state system. Some quantum error-correcting codes can also be easily constructed using the same technique. In view of the gate dependence on just global geometric features and the insensitivity to the state of cavity modes, the proposed quantum operations may result in high-fidelity quantum information processing.