Concurrence Measurement for the Two-Qubit Optical and Atomic States

Abstract

Concurrence provides us an effective approach to quantify entanglement, which is quite important in quantum information processing applications. In the paper, we mainly review some direct concurrence measurement protocols of the two-qubit optical or atomic system. We first introduce the concept of concurrence for a two-qubit system. Second, we explain the approaches of the concurrence measurement in both a linear and a nonlinear optical system. Third, we introduce some protocols for measuring the concurrence of the atomic entanglement system.

Quantum Classification Algorithm Based on Competitive Learning Neural Network and Entanglement Measure

“…A two-qubit system becomes an entangled states if the state of one qubit cannot be separated from the state of the other. Entanglement cannot be detected directly, so entanglement measures [49][50][51] were proposed to determine the degree of entanglement in a quantum system. Various measurements are proposed to measure the strength of the entanglement between two-qubit systems such as concurrence, witness, and negativity among others [50,52,53].…”

“…Various measurements are proposed to measure the strength of the entanglement between two-qubit systems such as concurrence, witness, and negativity among others [50,52,53]. However, the strength of entanglement in a two-qubit system is often measured using concurrence measure [50,51]. An arbitrary, pure two-qubit state has the form…”

“…The M z is a unitary operator that applies the CNOT gate between the qubits |u and |v followed by measuring the degree of entanglement in between through the operator D. The M z operator creates the entangled state |uv = α|00 + δ|11 , then it measures the concurrence between the qubits |u and |v as C > 0 through the operator D only if the input qubit |u is in the state |u = α|0 + δ|1 , while it leaves them disentangled in the state |uv = |00 , then it measures the concurrence value in between as C = 0 through the operator D only if the input qubit |u is in the state Some suggestions to implement the operator D using experimental setups are depicted in [51,55,59]. However, concretely in this paper, we propose to implement the operator D in the operator M z using Romero et al protocol [54].…”

Quantification of concurrence via weak measurement

“…Furthermore, measurements of concurrence that rely on relaxing the aforementioned PVM-criterion have been developed [16][17][18].…”

Direct measurement of nonlocal entanglement of two-qubit spin quantum states

“…In recent years, a number of theoretical and experimental schemes have been presented to direct measurement of concurrence for two-qubit entangled states 13 14 15 16 17 , including pure states and mixed states. These existing researches mainly focused on measurement of entanglement for two-photon entangled states with optical elements and atomic entangled states with cavity quantum electrodynamics system 18 19 . Besides the local entanglement, Zhou and Sheng discussed an efficient way for measuring nonlocal entanglement of atomic two-qubit pure states 20 .…”