The Essence of Entanglement

Brukner, Časlav; Żukowski, Marek; Zeilinger, Anton

doi:10.1007/978-3-030-77367-0_6

Cited by 19 publications

(13 citation statements)

References 44 publications

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“…To have knowledge of two systems being entangled is to be able to answer some questions on how these two systems are correlated. In other words, the information contained in a composite system can be divided into the information carried by individual systems, and the information contained in the correlations between observations made on individual subsystems [13]. Thanks to the knowledge balance principle, it is hence possible to either possess maximal knowledge about the states of subsystems -which results in their epistemic states being uncorrelated; or about the correlations between them, which is described as a correlated epistemic state -and an entangled one, if it is also a state of maximal knowledge.…”

Section: Meaning Of Entanglementmentioning

confidence: 99%

A consolidating review of Spekkens' toy theory

Hausmann,

Nurgalieva,

del Rio

2021

Preprint

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In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which features of quantum mechanics can be reproduced by such a foil theory. A prominent example is Spekkens' toy theory, which is based off a simple premise: "What if we took a common classical theory and added the uncertainty principle as a postulate?" In other words, the theory imposes an epistemic restriction on our knowledge about a physical system: only half of the variables can ever be known to an observer. Like good science fiction, from this simple principle a rich behaviour emerges, most notoriously when we compose several systems. The toy theory emulates some aspects of quantum non-locality, although crucially it is still a non-contextual model. In this pedagogical review we consolidate different approaches to Spekkens' toy theory, including the stabilizer formalism and the generalization to arbitrary dimensions, completing them with new results where necessary. In particular, we introduce a general characterization of measurements, superpositions and entanglement in the toy theory."Fiction writers, at least in their braver moments, do desire the truth: to know it, speak it, serve it. But they go about it in a peculiar and devious way, which consists in inventing persons, places, and events which never did and never will exist or occur, and telling about these fictions in detail and at length and with a great deal of emotion, and then when they are done writing down this pack of lies, they say, There! That's the truth."

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Section: Meaning Of Entanglementmentioning

confidence: 99%

A consolidating review of Spekkens' toy theory

Hausmann,

Nurgalieva,

del Rio

2021

Preprint

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“…The above expression will be used to find the postmeasurement states. By tracing out qubits 2 and 3 from (10) we immediately obtain the post-measurement state of (1, 4):…”

Section: Generalized Protocolmentioning

confidence: 99%

“…We begin with the definition of I (ρ) -the total information contained in correlations of a two-qubit state ρ. It is defined as [9,10]…”

Section: Trade-off Relationsmentioning

confidence: 99%

“…This suggests some kind of information-disturbance trade-off for Bob's measurements once we interpret "information" as information contained in correlations of a two-qubit state. In this paper we make this intuition precise in terms of an information theoretic measure of entanglement [8][9][10]. This measure, denoted by I (ρ), quantifies the total amount of information contained in correlations of a two-qubit state ρ (often we shall use information as short for "information contained in correlations" when there's no scope for confusion).…”

Section: Introductionmentioning

confidence: 99%

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Information-disturbance trade-off in generalized entanglement swapping

Bej

Ghosal²,

Das³

et al. 2020

Phys. Rev. A

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We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs (1, 2) and (3, 4), one performs an arbitrary joint measurement on (2, 3), so that (1, 4) now becomes correlated. We obtain trade-off inequalities between information gain in correlations of (1, 4) and residual information in correlations of (1, 2) and (3, 4) respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-two Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on (2, 3) can conserve information, even if, as in our example, the post-measurement states of all three pairs (1, 2), (3, 4), and (1, 4) become separable. This implies correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no information is lost in the process.

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“…Entanglement is one of the most intriguing characteristics that turns appart the quantum world from the classical world. Its fundamental importance in quantum foundations [1,2], together with its application in several areas, such as quantum information and quantum computation [3][4][5], has made the entanglement theory achieve great progress in recent decades. Moreover, there has been more and more interest in how entanglement behaves under relativistic settings [6].…”

Section: Introductionmentioning

confidence: 99%

Complete complementarity relations and its Lorentz invariance

Basso,

Maziero

2020

Preprint

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It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single particle states, a spin-momentum product state can be transformed into an entangled state. However, entanglement is just one of the aspects that completely characterizes a quantum system. The other two are known as the wave-particle duality. Although the entanglement entropy does not remain invariant under Lorentz boosts, and neither do the measures of predictability and coherence, we show here that these three measures taken together, in a complete complementarity relation (CCR), are Lorentz invariant. In addition, we explore relativist scenarios for single and two particle states, which helps understand the exchange of these different aspects of a quantum system under Lorentz boosts. For instance, by using discrete momentum states, we discuss the fact that for a spin-momentum product state to be transformed into an entangled state, it needs coherence between the momentum states. Otherwise, if the momentum state is completely predictable, the spin-momentum state remains separable, and the Lorentz boost will at most generate superposition between the spin states.

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The Essence of Entanglement

Cited by 19 publications

References 44 publications

A consolidating review of Spekkens' toy theory

A consolidating review of Spekkens' toy theory

Information-disturbance trade-off in generalized entanglement swapping

Complete complementarity relations and its Lorentz invariance

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