A Theory of Entanglement

Gudder, Stan

doi:10.12743/quanta.v9i1.115

Cited by 9 publications

(21 citation statements)

References 14 publications

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“…Proof. The proof of Corollary 4.4 repeats verbatim here, with the only addition that needs to be made is to verify that µ p is faithful when restricted to pure states, (a statement that for the entanglement number e was proved by Gudder [2]).…”

Section: P-number Of a State And Its Propertiesmentioning

confidence: 79%

“…Finally extend the definition of the entanglement number e to all mixed states of A ⊗ B using the convex roof construction. As Gudder proved, the entanglement number is faithful when restricted to pure states [2]. Moreover since the function f is norm-continuous, the entanglement number is norm continuous on pure states by Equation (54).…”

Section: Let T ⊂ {∅} ∪ ∞mentioning

confidence: 92%

“…A detailed review article [1] summarized our understanding of entanglement until 2009, but many new results have since appeared. Gudder in [2] introduced a general theory of entanglement which applies even to classical probability measures with discrete support. In the same article, he also introduced a quantity that he called the entanglement number which quantifies entanglement for classical probability measures as well as for density operators.…”

Section: Introductionmentioning

confidence: 99%

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Some Remarks on the Entanglement Number

Androulakis

McGaha

2020

Quanta

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Gudder, in a recent paper, defined a candidate entanglement measure which is called the entanglement number. The entanglement number is first defined on pure states and then it extends to mixed states by the convex roof construction. In Gudder's article it was left as an open problem to show that Optimal Pure State Ensembles (OPSE) exist for the convex roof extension of the entanglement number from pure to mixed states. We answer Gudder's question in the affirmative, and therefore we obtain that the entanglement number vanishes only on the separable states. More generally we show that OPSE exist for the convex roof extension of any function that is norm continuous on the pure states of a finite dimensional Hilbert space. Further we prove that the entanglement number is an LOCC monotone, (and thus an entanglement measure), by using a criterion that was developed by Vidal in 2000. We present a simplified proof of Vidal's result where moreover we use an interesting point of view of tree representations for LOCC communications. Lastly, we generalize Gudder's entanglement number by producing a monotonic family of entanglement measures which converge in a natural way to the entropy of entanglement.Quanta 2020; 9: 22–36.

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Section: P-number Of a State And Its Propertiesmentioning

confidence: 79%

Section: Let T ⊂ {∅} ∪ ∞mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Some Remarks on the Entanglement Number

Androulakis

McGaha

2020

Quanta

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“…,ρ k } is a set of quantum states (described by their density matrix operators, cf. (Belinfante, 1980;Hughston et al, 1993;de Gosson, 2018)) that are drawn from the probability distribution {p 1 , p 2 , . .…”

Section: Holevo's Bound On Accessible Classical Information From Quanmentioning

confidence: 99%

Quantum information theoretic approach to the mind–brain problem

Georgiev

2020

Progress in Biophysics and Molecular Biology

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The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind-brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the underlying brain processes toward desired behavior. Yet, this setback does not establish that consciousness is non-physical. Modern quantum physics affirms the interplay between two types of physical entities in Hilbert space: unobservable quantum states, which are vectors describing what exists in the physical world, and quantum observables, which are operators describing what can be observed in quantum measurements. Quantum no-go theorems further provide a framework for studying quantum brain dynamics, which has to be governed by a physically admissible Hamiltonian. Comprising consciousness of unobservable quantum information integrated in quantum brain states explains the origin of the inner privacy of conscious experiences and revisits the dynamic timescale of conscious processes to picosecond conformational transitions of neural biomolecules. The observable brain is then an objective construction created from classical bits of information, which are bound by Holevo's theorem, and obtained through the measurement of quantum brain observables. Thus, quantum information theory clarifies the distinction between the unobservable mind and the observable brain, and supports a solid physical foundation for consciousness research.

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“…There are various justifications for the definition (8) [10]. One is that if the distribution λ is peaked near 1, then e(ψ) should be near 0 and if λ is spread fairly equally, then e(ψ) should be large.…”

Section: An Entanglement Measurementioning

confidence: 99%

Quantum Entanglement: Spooky Action at a Distance

Gudder¹

2020

Quanta

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Quantum entanglement is an important resource in quantum information technologies. Here, we study and characterize in a precise mathematical language some of the weird and nonintuitive features of quantum entanglement. We begin by illustrating why entanglement implies action at a distance. We then introduce a simple criterion for determining when a pure quantum state is entangled. Finally, we present a measure for the amount of entanglement for a pure state.Quanta 2020; 9: 1–6.

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A Theory of Entanglement

Cited by 9 publications

References 14 publications

Some Remarks on the Entanglement Number

Some Remarks on the Entanglement Number

Quantum information theoretic approach to the mind–brain problem

Quantum Entanglement: Spooky Action at a Distance

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