How to observe and quantify quantum discord in electronic systems Igor Lerner & Matt Hunt (Birmingham) Igor Yurkevich (Aston Uni, UK) Yuval Gefen (Weizmann Inst, Israel)
Overview Quantum correlations in bipartite systems: entanglement and beyond Discord: quantumness of separable states related to conditional von Neumann entropy Detecting and quantifying discord via interference correlations Quantum Measurements, ICTP, 2019
Bipartite system: pure state Von Neumann entropy S = - Tr r ln r =0 - no uncertainty Quantumness (or its absence) reveals in partitioning the system Quantum Measurements, ICTP, 2019
Entanglement of pure state Quantum Measurements, ICTP, 2019
Bipartite system: mixed state Is AB entangled or not? – not necessarily obvious, e.g. Werner state: Generically, a mixed state of a bipartite system is not entangled iff (Werner, ’89) However, such a separable mixed state can still have quantumness exemplified by quantum discord. (Ollivier and Zurek, ’01; Henderson and Vedral, ‘01) Quantum Measurements, ICTP, 2019
Classical mutual information The concepts of quantum discord comes from comparing quantum and classical conditional entropies in bipartite systems. Shannon entropy of system AB with joint probability distribution p(a,b) : Quantum Measurements, ICTP, 2019
Quantum mutual information Quantum analogue: I,J(A:B) → I,J (AB) with H→S : However, J A ( r AB ) is more tricky as a basis-independent definition of conditional entropy requires optimization over all possible measurements over ‘passive’ subsystem B. So the more precise definition is minimizing ignorance about A, i.e. picking the best measurement basis Quantum Measurements, ICTP, 2019
Quantum discord (Ollivier and Zurek, ’01; Henderson and Vedral, ‘01) Quantum Measurements, ICTP, 2019
Quantum discord Alternative expression for quantum discord Quantum Measurements, ICTP, 2019
Pure state: discord ≡ entanglement If a mixed state is entangled, it is always discorded – D adds little. Hence, our main interest is in discord of separable – unentangled – states. Quantum Measurements, ICTP, 2019
Discord of mixed separable state Here D A =0 for any q. For q=0,p the subsystems are totally uncorrelated and D B =0 For q=p/2 , the classical mutual information is maximal but it is entirely classical and D B =0 again. Quantum Measurements, ICTP, 2019
Discord of mixed separable state This state is A -non-discorded in either a trivial case – all | a n > coincide, or when all | a n > are orthogonal. Otherwise, they are discorded independently of B Our aim: to find linear in r characteristics of a bipartite system that detect and quantify discord Quantum Measurements, ICTP, 2019
Entanglement witness How to detect and quantify the remaining quantumness – discord – Q. linearly, as Tr ( r …) , without full or partial quantum tomography. Theorem: no linear witness of discord ( R. Rahimi and A. SaiToh, 2010 ) Way around: repeated measurements of certain correlations. Quantum Measurements, ICTP, 2019
Discord via correlations Quantum Measurements, ICTP, 2019
Visibility as discord witness Quantum Measurements, ICTP, 2019
Measuring setup System preparation Evolution & measurement Quantum Measurements, ICTP, 2019
Input state discorded nondiscorded Quantum Measurements, ICTP, 2019
Visibility pattern Quantum Measurements, ICTP, 2019
Discord witnesses (b) 4p 4p d is corded 3p 3p a a 2p 2p 0p 0p 00 00 0 p 2p 3p 4p 0 p 2p 3p 4p b b (b) 4p 3p a 2p 0p nondiscorded 00 0 p 2p 3p 4p b Quantum Measurements, ICTP, 2019
Quantifying discord Quantum Measurements, ICTP, 2019
Summary • Discord is hard to measure. Alternatives (geometric discord) are based on full or partial quantum tomography – hardly extendable to condensed matter systems • The proposed discord witness – the visibility in (linear in r ) interference pattern • The proposed quantifier gives results similar to the original. Quantum Measurements, ICTP, 2019
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