[Paper Review] Quantum advantage by weak measurements

Lin-Ping Huai, Bo Li+2 more|arXiv (Cornell University)|May 28, 2013

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper demonstrates that weak measurements can generate additional quantum correlation—termed 'super discord'—which acts as a resource for quantum advantage in information encoding. By showing that this enhanced quantum correlation can be fully consumed during coherent quantum interactions, the authors prove weak measurements provide a greater quantum advantage than standard projective measurements, particularly in pure entangled and Bell-diagonal states.

ABSTRACT

Weak measurements may result in extra quantity of quantumness of correlations compared with standard projective measurement on a bipartite quantum state. We show that the quantumness of correlations by weak measurements can be consumed for information encoding which is only accessible by coherent quantum interactions. Then it can be considered as a resource for quantum information processing and can quantify this quantum advantage. We conclude that weak measurements can create more valuable quantum correlation.

Motivation & Objective

• To investigate whether the extra quantum correlation induced by weak measurements can serve as a resource for quantum advantage.
• To compare the quantum advantage achievable via weak measurements versus standard projective measurements in bipartite quantum systems.
• To establish that super discord from weak measurements can be consumed during coherent information encoding, thus quantifying its operational value.
• To analyze the behavior of quantum advantage in specific states, including two-qubit pure entangled states and Bell-diagonal states.
• To demonstrate that weak measurements reveal more quantum advantage than projective measurements, especially in Werner and Bell-diagonal states.

Proposed method

• Define quantum advantage as the difference between discord consumption during coherent encoding and classical correlation, following the operational framework of Mile Gu.
• Introduce weak measurement via a positive operator-valued measure (POVM) with a tunable strength parameter $ x $, modeling partial collapse of the quantum state.
• Compute the quantum discord using weak measurement outcomes, deriving expressions for super discord as a function of measurement strength $ x $ and state parameters.
• Analyze the mutual information $ I( ho_{ab}) $, classical correlation $ J( ho_{ab}) $, and quantum discord $ D( ho_{ab}) $ under weak measurement, using von Neumann entropy and eigenvalue decomposition.
• Use the Werner state and Bell-diagonal state as test cases to compare quantum advantage via weak vs. projective measurements, with analytical expressions for $ riangle I_p $ and $ riangle I_w $.
• Numerically and analytically evaluate the quantum advantage as a function of state parameters ($ c_1, c_2, c_3 $) and measurement strength $ x $, showing periodic behavior in $ heta $.

Experimental results

Research questions

• RQ1 Can the additional quantum correlation generated by weak measurements be consumed during coherent quantum information encoding?
• RQ2 Does weak measurement provide a greater quantum advantage than standard projective measurement in bipartite quantum systems?
• RQ3 How does the strength of weak measurement ($ x $) affect the quantum advantage in Bell-diagonal and Werner states?
• RQ4 Is the super discord induced by weak measurement operationally useful as a resource in quantum information processing?
• RQ5 What is the relationship between quantum advantage, entanglement, and quantum discord in states like Werner and Bell-diagonal states?

Key findings

• Weak measurements generate a form of enhanced quantum correlation—'super discord'—that exceeds standard quantum discord under projective measurements.
• For two-qubit pure entangled and Bell-diagonal states, super discord from weak measurements can be fully consumed during coherent encoding, demonstrating its role as a resource.
• In Bell-diagonal states with $ c_1=0.15, c_2=0.03, c_3=0.7 $, weak measurement yields a quantum advantage greater than that from projective measurement, especially for $ x > 3 $ and $ heta = n heta $.
• For Werner states, the quantum advantage via weak measurement ($ riangle I_w $) exceeds that of projective measurement ($ riangle I_p $) across all $ c $ values when measurement strength $ x = 0.7 $, with $ riangle I_w $ decreasing as $ x $ increases.
• When measurement strength $ x > 2.5 $, $ riangle I_w $ approaches $ riangle I_p $, indicating diminishing quantum advantage from weak measurement at high $ x $, consistent with reduced coherence.
• The quantum advantage from weak measurement is monotonic with respect to entanglement and quantum discord in Werner states, confirming its operational relevance.