Golden states in resource theory of superposition

T., Şenyaşa, Hüseyin; Torun, Gökhan

doi:10.1103/physreva.105.042410

Cited by 4 publications

(11 citation statements)

References 34 publications

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“…We now proceed to our main result in which we focus our attention on the resource states with maximal superposition. This essential subject was particularly discussed in [60], where the eigensystems of the constructed overlap matrices involve information on the existence of maximal superposition states. Here, we show that the same results [60] can be obtained forthwith by LSO.…”

Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

“…This essential subject was particularly discussed in [60], where the eigensystems of the constructed overlap matrices involve information on the existence of maximal superposition states. Here, we show that the same results [60] can be obtained forthwith by LSO. Figure 2 illustrates the way that we apply to realize the form of the states with maximal superposition, i.e.…”

Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

“…Figure 2 illustrates the way that we apply to realize the form of the states with maximal superposition, i.e. golden states in RTS [60].…”

Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

“…Also, a quantum operation Φ(•) is called superposition-free if it is trace preserving and can be written such that Φ(ρ) = ∑ n K n ρK † n , where all K n are free. For further reading and details, we refer the reader to [18,54,60].…”

Section: Resource Theory Of Superpositionmentioning

confidence: 99%

“…Central to our study is the characterization of the states with maximal superposition, with the potential to illuminate the transformation of superposition states. The recent work of [60] has established a structural way to investigate maximal states of RTS, i.e. golden states, utilizing the eigenvalues and eigenvectors of the Gram matrix constructed from the given set of arbitrary (nonorthogonal) basis states.…”

Section: Introductionmentioning

confidence: 99%

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Coherence, superposition, and Löwdin symmetric orthogonalization

Torun

2023

J. Phys. A: Math. Theor.

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The notions of coherence and superposition are conceptually the same; however, an important distinction exists between their resource-theoretic formulations. Namely, while basis states are orthogonal in the resource theory of coherence, they are not necessarily orthogonal in the resource theory of superposition. Owing to the nonorthogonality, the manipulation and characterization of superposition states require significant efforts. Here, we demonstrate that the L"{o}wdin symmetric orthogonalization (LSO) method offers a useful means for characterizing pure superposition states. The principal property of LSO is that the structure and symmetry of the original nonorthogonal basis states are preserved to the greatest extent possible, which prompts us to study the role of LSO in identifying the hierarchical relations of resource states. Notably, we reveal that the maximally coherent states turn into the states with maximal superposition with the help of LSO: in other words, they are equivalent under the action of symmetric orthogonalization. Our results facilitate further connections between coherence and superposition, where LSO is the main tool.

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Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

“…Figure 2 illustrates the way that we apply to realize the form of the states with maximal superposition, i.e. golden states in RTS [60].…”

Section: Main Result: Equivalence Of Maximally Resourceful Statesmentioning

confidence: 99%

Section: Resource Theory Of Superpositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%