I started working on coherence and entanglement. At a point, I became confused between the concepts of entanglement and coherence where an author texted it the same however, they are still considered different by many authors. If anyone can explain, please answer this
The two phenomena are greatly interrelated in the sense that, if one is lost another is lost too.
Entanglement appraises that two or more entangled objects cannot be represented separately while in the coherence term, the superposition of two or more objects is defined. Thus, I think the definitions are closely related and are two sides of the same coin.
Sadam Hussain Please follow the link, I hope it will clear everything for you.
https://phys.org/news/2015-06-physicists-quantum-coherence-entanglement-sides.html
The short answer is, all kinds of quantum correlations satisfy the conditions: quantum coherence ⊇ quantum discord ⊇ quantum entanglement ⊇ quantum steering ⊇ Bell non-locality. Therefore, coherence is considered to be the most general measure.
Relationship Between Entanglement and Coherence in Some Two-Qubit States
Article Relationship Between Entanglement and Coherence in Some Two-...
Article Experimental hierarchy and optimal robustness of quantum cor...
Article Steering, Entanglement, Nonlocality, and the Einstein-Podols...
Abbas Hassasfar
In general, all kinds of quantum correlations satisfy the conditions: quantum coherence ⊇ quantum discord ⊇ quantum entanglement ⊇ quantum steering ⊇ Bell non-locality, where, for example, P ⊇ Q means P is the superset of Q. This reveals that steerable states are a strict subset of the entangled states and a strict superset of the states that may exhibit Bell non-locality and similarly to the others, the so-called hierarchy relations of the quantum correlations.
For more details consult the following references:
Article Hierarchy of quantum correlations using a linear beam splitter
Article Gaussian entanglement generation from coherence using beam-splitters
In some ways, all kind of quantum correlations like entanglement are just subsets of quantum coherence (QC). In fact, QC appears to be the more fundamental than entanglement. This is because:
1. QC can be defined for each individual quantum system but entanglement can not (it needs at least two parties).
2. Consider an entangled state : a |00> + b |11>. Obviously, each subsystems is in a superposition state. Without such a superposition (coherence) of individual parts, entanglement will be meaningless.
Best.
Quantum coherence originates from the superposition of quantum states i.e. anytime you have a superposition state (not a pure state) then you have coherence terms in your density matrix whereas, entanglement is a kind of superposition of states between at least two part of the system that it is not separable. In other words, quantum entanglement is a special case of quantum coherence but in a two-partite or multi-partite system. Notice that, a fully mixed state does not possess quantum coherence.
What quantum entanglement? considering that it is possible to identify (and distinguish!) between a mathematical (or spurious) entanglement and a physical entanglement. Identification of a mathematical entanglement (in a mathematical model) does not necessarily correspond to the existence of a corresponding physical entanglement (in a quantum system).
You may read the following article in the context of your question.
Entanglement and Superposition Are Equivalent Concepts in Any Physical Theory, PHYSICAL REVIEW LETTERS 128, 160402 (2022).
Dear Doctor
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Quantum Coherence and Intrinsic Randomness
Xiao Yuan, Qi Zhao, Davide Girolami, Xiongfeng Ma (2019)
"Abstract—The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose informationtheoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as the resource for the intrinsic randomness in the measurement outcomes of a state in the computational basis. We observed in our previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a (classical) correlated party about the system measurement outcome. In this work, we re-derive the result from a quantum point of view and then connect the intrinsic randomness to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there does not exist bound coherent states, these two intrinsic randomness quantified by coherence of formation and the relative entropy of coherence are different. Interestingly, we show that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system."
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