Generation and stabilization of Bell states via repeated projective measurements on a driven ancilla qubit

Abstract

A protocol is proposed to generate Bell states in two non-directly interacting qubits by means of repeated measurements of the state of a central ancilla connected to both qubits. An optimal measurement rate is found that minimizes the time to stably encode a Bell state in the target qubits, being of advantage in order to reduce detrimental effects from possible interactions with the environment. The quality of the entanglement is assessed in terms of the concurrence and the distance between the qubits state and the target Bell state is quantified by the fidelity. I. INTRODUCTIONPreparing entangled states is a basic requirement for many quantum technologies [1,2], notably for quantum information [3] and quantum metrology [4,5]. Being entanglement an exquisite non-classical feature, its quantification is of fundamental interest [6][7][8]. Several protocols to generate entangled states have been developed to date, including control of quantum dynamics [9-12] and engineered dissipation [13][14][15][16][17][18][19][20][21][22]. An intriguing route towards this goal is to exploit the quantum backaction of measurements performed on a part or on the whole system. In this context, different schemes have been proposed [23][24][25][26][27][28]55] and implemented [29][30][31] which rely on the use of a parity meter on the collective state of two qubits. The introduction of a feedback control based on the readout of a continuous weak measurement of parity provides further means to entangle bipartite systems [32][33][34][35]. A parity meter of the state of two qubits, α and β, discriminates if they are in an even or odd parity collective state, associated to the two eigenvalues 1 and −1 of the parity operator σ α z ⊗ σ β z , respectively. Consider the one-qubit state |+ = (| ↑ + | ↓ )/ √ 2 expressed in the eigenbasis of σ z . A parity measurement on the two-qubit system prepared in the separable joint state |+ α |+ β projects the system onto one of the Bell states |Φ + = (| ↑↑ +| ↓↓ )/ √ 2 arXiv:1802.04839v2 [quant-ph]

SU(2) Decomposition for the Quantum Information Dynamics in 2d-Partite Two-Level Quantum Systems

“…Thus, the Bell basis for two-level bipartite systems has been shown to fit in the U(1) × SU(2) 2 decomposition of SU (4). Despite the added complexity to manage non-local states, recent work has moved towards the control of entangled states [18]. This basis works as a universal basis for the Heisenberg-Ising interaction, including an external magnetic field in any specific direction on a couple of qubits [11][12][13].…”

“…A direct but large analysis shows that by fitting (18) to (11), the Hamiltonian should be reduced to the forms shown in Table 1 (assuming always h 0 2d 4 = 0 and H 0 = ∑ 3 j=1 h jj σ j ⊗ σ j ). The first column shows the pairs arrangement to construct the blocks.…”

“…Still, if two correspondent k elements are considered (local interactions on each element of a correspondent pair), they still generate only one non-zero row (each one with the two terms explained before). Although there are 2d possibilities to select the position s = k in (22), they do not count as separate blocks because they appear in other entries in (18). Instead, each term in non-correspondent terms will appear in a different non-zero row, giving d non-zero rows as total.…”

“…That original expression is highly convenient for the development of the current work because it allows it to be easily connected with the form of the Hamiltonian (1) in the same terms, allowing the important result to be easily obtained (18). Nevertheless, a more simple expression could be given for the understanding of such states.…”

SU(2) Decomposition for the Quantum Information Dynamics in 2<em>d</em>-Partite Two-Level Quantum Systems

“…Thus, the Bell basis for two-level bipartite systems has shown fit in the U(1) × SU(2) 2 decomposition of SU (4). Despite the added complexity to manage non-local states, recent work goes in that direction, the control of entangled states [15]. This basis works as a universal basis for the Heisenberg-Ising interaction including an external magnetic field in any specific direction on a couple of qubits [8][9][10].…”