Abstract
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges etal., Science 364, 260 (2019)SCIEAS0036-807510.1126/science.aau4963].
Highlights
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix
We propose and experimentally demonstrate conditions for mixed-state entanglement and measurement protocols based on the positive partial transpose (PPT) condition [2, 5, 19]
In the SM [23], we present additional simulations showing the power of the p3 -PPT condition, in comparison with the negativity and the condition based on purities of nested subsystems
Summary
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. Developing protocols which detect and quantify mixed-state entanglement on intermediate scale quantum devices is an outstanding challenge. We propose and experimentally demonstrate conditions for mixed-state entanglement and measurement protocols based on the positive partial transpose (PPT) condition [2, 5, 19].
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