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arXiv:1212.5338 · Physical Review A

Identifying quantumness via addition-then-subtraction operation

Su‐Yong Lee, Changsuk Noh, Dagomir Kaszlikowski

Published Jul 8, 2013• 5 citations
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Abstract

We propose a measure of quantumness based on an addition-then-subtraction operation. We demonstrate how this measure can distinguish between classical and bosonic particles by investigating in detail multiparticle bosonic systems. Experimental schemes implementing this measure for bosons in all-optical and atom-cavity systems are provided. We also apply this measure to single-mode fermionic systems.

DOI
10.1103/physreva.88.013806

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We propose a measure of quantumness based on an addition-then-subtraction operation. We demonstrate how this measure can distinguish between classical and bosonic particles by investigating in detail multiparticle bosonic systems. Experimental schemes implementing this measure for bosons in all-optical and atom-cavity systems are provided. We also apply this measure to single-mode fermionic systems.
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We propose an experiment to directly prove the commutation relation between bosonic annihilation and creation operators, based on the recent experimental success in single-photon subtraction and addition. We devise a single-photon interferometer to realize coherent superpositions of two sequences of photon addition and subtraction. Depending on the interference outcome, the commutation relation is directly proven or a highly nonclassical state is produced. Experimental imperfections are assessed to show that the realization of the scheme is highly feasible.
We propose a cavity QED-based scheme to observe the noncommutativity between the creation and annihilation operators. By conditional measurement after the atom-field interaction in a cavity, it is possible to achieve a photon-added-then-subtracted state and a photon-subtracted-then-added state, which have different statistical properties. This scheme has the advantages of simple analytical results and much higher generation probabilities. We show that the ideal results of one-cycle photon addition and subtraction are approached in the short time limit. We also discuss the possible implementation scheme.
The indistinguishability of particles is an important feature of quantum mechanics. To account for indistinguishability, identical particles are described as inherently correlated. In this paper we study a method of transforming these correlations into operationally accessible entanglement with single-particle subtractions. We provide specific protocols to turn the bosonic symmetrization into various classes of entanglement. Moreover, we explain why analogous schemes cannot work for fermions. These results provide a new perspective on manipulating quantum states with heralded subtraction.
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Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.