Operational Determination of Multiqubit Entanglement Classes via Tuning of Local Operations

Abstract

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 GHZ 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 welldefined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.PACS numbers: 42.50. Ex, 03.65.Ud, 03.67.Bg, 42.50.Dv Entanglement is a distinctive property of quantum physics associated with the nonseparable character of multipartite quantum systems. For the case of two-qubit systems, entanglement is well understood and can be precisely quantified [1]. Apart from the trivial disentangled case, three qubits possess two genuine tripartite inequivalent entanglement classes [2,3]. Efforts have been done recently towards higher number of qubits [4,5,6], including an inductive method [7], though so far no comprehensive and scalable classification has been developed. In this letter, we introduce a physical setup consisting of N emitters, incoherently radiating single photons that may be absorbed remotely by detectors equipped with polarizers and producing long-lived multiqubit entangled states among the emitters. We show that it is possible to associate well-defined sets of locally tuned polarizer orientations with multiqubit entanglement classes, allowing their monitoring in an operational manner. Hereby, multipath quantum interferences, associated with qubit permutation symmetry, play a key role in explaining the underlying physics.We consider a chain of N equally separated single photon emitters, say trapped neutral atoms, trapped ions, quantum dots, or any other equivalent physical system with access to similar behaviour. Each emitter defines a three-level Λ system, where |e denotes the excited state and the two long-lived sublevels, |+ and |− , define a qubit. We assume that the transitions between the excited state and the two lower sublevels have an equal wavenumber and dipole moment, and that they are circularly polarized, σ + and σ − , respectively. Figure 1 exemplifies the N -emitter case discussed throughout this paper. All emitters are initially excited and we will study the cases in which all spontaneously emitted photons are detected by N detectors located in the far-field re- gion, each of them being equipped with a polarization filter in front. The far-field detection ensures the erasure of which-way information of the arriving photons, and the polarizers allow the generation of quantum superpositions of the lower atomic states when considering arbitrary polarizations. As a consequence each photodetection event projects the emitters onto linear combinations of the long-lived states |+ and |− [8]. This results at the end in a coherent superposition between the qubit states |±, . . . , ± . The indeterminacy of which detector

Limits to multipartite entanglement generation with bosons and fermions

“…Manifold further strategies for the creation of entangled states were proposed [32][33][34][35][36][37][38], which promise to carry on the experimental achievements [1,13,14,18,31]; but although all schemes share the same physical ingredients, no common framework permits a direct comparison. With the increasing complexity of many-photon setups, a general framework is highly desirable to achieve high success rates, a low number of components, and a comparison of competing approaches to entanglement generation [37,38].…”

Entangled symmetric states ofNqubits with all positive partial transpositions

“…Another motivation comes from the recent experimental realizations of symmetric states of many-qubits, as for instance, the six-qubit Dicke states [20] or the eight-qubit GHZ states [21] (see also Ref. [22] in this context).…”

Deterministic generation of arbitrary symmetric states and entanglement classes

“…We point out that one can directly map the c k coefficients in this state to the corresponding symmetric entanglement classes through Vieta's formulas [10,11,14]. We will use this property at the end of the paper to establish a correspondence between entanglement classes for symmetric states and experimental parameters in quantum optics systems.…”

“…In our specific example, the set of parameters α i , β i , i = 0, 1, 2, 3, associated with local gates and conditional rotations [1], determines the c k numbers, and it is attainable, in the trapped-ion example, with the gate toolbox introduced in [36,37]. Then, one maps the c k coefficients to the corresponding entanglement class through Vieta's formulas [10,11,14].…”

“…On the other hand, an increasing interest for operational entanglement classifications, with direct connection to experimental setups, has given rise to proposals based on atoms or ions coupled by spontaneously emitted photons and interference in the detection process [14,15]. However, this kind of proposals have a small success probability that decreases exponentially with the number of qubits, restricting their scalable implementation [16].…”