Parameterized entanglement measures with computable lower bounds

Mahboobeh Moslehi, Hamid Reza Baghshahi, Sayyed Yahya Mirafzali

Ning Yang, Yu Guo, Shuanping Du

Although numerous measures of entanglement have been proposed so far, the calculation of a given faithful entanglement measure is a hard work since it is always involved in some optimization process. It is, therefore, important to estimate the lower bound of a given entanglement measure for an arbitrary quantum state. This results in a subject of intensive mathematical research. In particular, along this line, the lower bounds of concurrence or other measures that are induced from concurrence have been explored a lot. Here, we investigate the lower bounds of two kinds of entanglement monotones, i.e., $q$-concurrence ($q>1$) and $α$-concurrence ($0<α<1$), or termed the parameterized entanglement monotone together. We obtain, in the light of the informationally complete ($N$, $M$)-positive operator-valued measure [($N$, $M$)-POVM], the lower bounds for the case of $\frac12<α<1$, $1<q<2$ for two-qudit states, and the case of $2\leqslant q<3$ for two-qubit states. We list several examples which show that the lower bounds based on ($N$, $M$)-POVM outperform that of GSIC-POVM and SIC-POVM, and all these measurement based bounds are better then the ones induced by positive partial transpose (PPT) and realignment criteria in literature. In addition, we obtain an analytical formula of the parameterized entanglement monotone with $\frac12<α<1$ and $1<q<2$ for the isotropic state.

Zhi-Wei Wei, Ming-Xing Luo, Shao-Ming Fei

Remigiusz Augusiak, Maciej Lewenstein

Zhi-Wei Wei, Shao-Ming Fei

Abstract We propose a novel parameterized entanglement measure α -concurrence for bipartite systems. By employing positive partial transposition and realignment criteria, we derive analytical lower bounds for the α -concurrence. Moreover, we calculate explicitly the analytic expressions of the α -concurrence for isotropic states and Werner states.

Karl Mayer, Charlie Baldwin

We define scalable benchmarks for two important quantum subroutines, namely the quantum Fourier transform (QFT) and the multi-controlled-Z gate. Our benchmarks are based on applying the subroutines to a set of states that are sufficient for lower-bounding the process fidelity from the set of measured output state fidelities. By randomly sampling from the set of input states, the lower boundonthe process fidelity can be estimated. We implement the QFT and multi-controlled-Z circuits with up to 20 and 12 qubits, respectively, on the Quantinuum H1-1 quantum computer. Our circuits make use of parameterized-angle entangling gates, which for these circuits reduces the number of two-qubit gates significantly.