Entanglement for all quantum states

Torre, Alícia; Goyeneche, Dardo; Leitão, Lauro

doi:10.1088/0143-0807/31/2/010

Cited by 38 publications

(45 citation statements)

References 9 publications

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“…Thus entanglement in pairs of Glauber coherent states is consistent with previous evidences of nonclassical behavior as revealed by negativity of numberphase Wigner functions [4], nonclassical statistics in photon number detection [5], and unbalanced double homodyne detection [6], as well as other results [7]. This also fits with the idea that entanglement may be a more widespread property than naively expected [8][9][10].…”

Section: Introductionsupporting

confidence: 90%

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Entanglement between total intensity and polarization for pairs of coherent states

Sanchidrián-Vaca¹,

Luis

2018

Phys. Rev. A

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We examine entanglement between number and polarization, or between number and relative phase, for pairs of coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode Hilbert space in a larger space to get a well-defined factorization of the number-phase variables. This can be regarded as a kind of proto-entanglement that can be extracted and converted into real particle entanglement via feasible experimental procedures. In particular this reveals interesting entanglement properties of pairs of coherent states.

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Section: Introductionsupporting

confidence: 90%

“…Let us now use the covariance criterion studied in Ref. [8] that establishes that for pure states there is entanglement between A and B variables provided that…”

Section: B Covariancementioning

confidence: 99%

Entanglement between total intensity and polarization for pairs of coherent states

Sanchidrián-Vaca¹,

Luis

2018

Phys. Rev. A

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“…In their first example Torre et al 6 consider a quantum system described by a separable quantum state ψ depending on position coordinates . The local position observables X 1 and X 2 are represented by 1 X X I  and 2 X I X  where X is a position operator.…”

Section: Not All Quantum States Are Entangledmentioning

confidence: 99%

Operational approach to entanglement and how to certify it

Kupczyński

2016

Int. J. Quantum Inform.

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Entangled physical systems are an important resource in quantum information. Some authors claim that in fact all quantum states are entangled. In this paper we show that this claim is incorrect and we discuss in operational way differences existing between separable and entangled states. A sufficient condition for entanglement is the violation of Bell-CHSH-CH inequalities and/or steering inequalities. Since there exist experiments outside the domain of quantum physics violating these inequalities therefore in the operational approach one cannot say that the entanglement is an exclusive quantum phenomenon. We also explain that an unambiguous experimental certification of the entanglement is a difficult task because classical statistical significance tests may not be trusted if sample homogeneity cannot be tested or is not tested carefully enough.

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“…Previously, special cases of this theorem proved the existence of tensor product structures for which any pure state is separable [9] and of observables that will detect non-local correlations in any pure state [4].…”

Section: Lemma 4 (Vandermonde Determinantmentioning

confidence: 99%

“…The algebra of observables must be partitioned into subalgebras that satisfy two mathematical requirements, the subalgebras must be independent and complete (see Corollary 3 for a precise formulation of Zanardi's Theorem), and one physical requirement, the subalgebras must be locally accessible. Such observableinduced partitions of the Hilbert space have been referred to as virtual subsystems and can be thought of as a generalization from entanglement between subsystems to entanglement between degrees of freedom (see also [3,4]). This mathematical framework has found applications to studies of multi-level encoding [5], decoherence [6], operator quantum error correction [7], entanglement in fermionic systems [8], single-particle entanglement [9,10], and entanglement in scattering systems [11].…”

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confidence: 99%

Observables can be tailored to change the entanglement of any pure state

Harshman

Ranade

2011

Phys. Rev. A

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We show that for a finite-dimensional Hilbert space, there exist observables that induce a tensor product structure such that the entanglement properties of any pure state can be tailored. In particular, we provide an explicit, finite method for constructing observables in an unstructured d-dimensional system so that an arbitrary known pure state has any Schmidt decomposition with respect to an induced bipartite tensor product structure. In effect, this article demonstrates that in a finite-dimensional Hilbert space, entanglement properties can always be shifted from the state to the observables and all pure states are equivalent as entanglement resources in the ideal case of complete control of observables.PACS numbers: 03.65.Aa, 03.65.UdThe entanglement of a quantum state is only defined with respect to a tensor product structure within the Hilbert space that represents the quantum system. In turn, a tensor product structure of the Hilbert space is induced by the algebra of observables. Zanardi and colleagues [1,2] have provided criteria for the algebra of observables of a finite-dimensional system to induce a tensor product structure. The algebra of observables must be partitioned into subalgebras that satisfy two mathematical requirements, the subalgebras must be independent and complete (see Corollary 3 for a precise formulation of Zanardi's Theorem), and one physical requirement, the subalgebras must be locally accessible. Such observableinduced partitions of the Hilbert space have been referred to as virtual subsystems and can be thought of as a generalization from entanglement between subsystems to entanglement between degrees of freedom (see also [3,4]). This mathematical framework has found applications to studies of multi-level encoding [5], decoherence [6], operator quantum error correction [7], entanglement in fermionic systems [8], single-particle entanglement [9,10], and entanglement in scattering systems [11].In this Letter, we extend this mathematical framework and prove what we call the Tailored Observables Theorem (Theorem 6): observables can be constructed such that any pure state in a finite-dimensional Hilbert space H = C d has any amount of entanglement possible for any given factorization of the dimension d of H. This means all pure states are equivalent as entanglement resources in the ideal case of complete control of observables. To establish the framework, we provide a brief, relatively self-contained introduction to Zanardi's Theorem and obtain some necessary preliminary results about observable algebras in finite dimensions. We then prove Theorem 6, which applies to bipartite tensor product structures, and present an illustrative example. We will also provide a corollary of the theorem (Corollary 7) applied to multipartite tensor product structures. Before delving into the technical details, we present a more intuitive discussion of this result. this Hilbert space could represent states of a quantum system composed from N subsystems each represented by Hilbert spaces H i = C ki . Fo...

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Entanglement for all quantum states

Cited by 38 publications

References 9 publications

Entanglement between total intensity and polarization for pairs of coherent states

Entanglement between total intensity and polarization for pairs of coherent states

Operational approach to entanglement and how to certify it

Observables can be tailored to change the entanglement of any pure state

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