Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables

Area of Science:

• Quantum mechanics
• Quantum information science

Background:

• Entanglement is a key quantum phenomenon crucial for quantum information science.
• Detecting entanglement without full quantum state tomography is a significant theoretical and experimental challenge.

Purpose of the Study:

• To investigate the possibility of universal entanglement detection using only single-copy measurements.
• To establish fundamental limits on entanglement detection methods in quantum mechanics.

Main Methods:

• Proving a no-go theorem for nonadaptive single-copy measurement schemes.
• Simulating and experimentally verifying a previously published protocol for entanglement detection.
• Analyzing protocols for their necessity of full state tomography.

Main Results:

• A no-go theorem demonstrates that universal entanglement detection is impossible with nonadaptive single-copy measurements.
• A prior experimental protocol, claimed to avoid full state tomography, was shown to necessitate it.
• Fundamental limitations of single-copy measurements for entanglement detection were revealed.

Conclusions:

• Single-copy measurements alone cannot achieve universal entanglement detection without full state tomography.
• Existing protocols may inadvertently require full state tomography, contrary to initial claims.
• The findings provide a framework for detecting other quantum state properties, like positivity of partial transpose.