Tomography is necessary for universal entanglement detection with single-copy observables

TL;DR

This paper proves that universal entanglement detection cannot be achieved with non-adaptive single-copy measurements without full state tomography, highlighting fundamental limits and analyzing a previous experiment.

Contribution

It establishes a no-go theorem for non-adaptive single-copy entanglement detection and critically examines an experimental claim, demonstrating the necessity of full state reconstruction.

Findings

No universal entanglement detection with non-adaptive single-copy measurements.

Experimental data can reconstruct the quantum state, contradicting claims of entanglement detection without tomography.

Provides a framework for studying other quantum state properties like positivity of partial transpose.

Abstract

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the $k$-symmetric extendibility.