Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange’s identity and wedge product

Bhaskara, Vineeth S.; Panigrahi, Prasanta K.

doi:10.1007/s11128-017-1568-0

Cited by 41 publications

(44 citation statements)

References 28 publications

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“…This allows us to draw a simple connection to the notion of a pure density matrix, since even though the 1RDM is specifically simple in structure, it has in this case still a purity smaller than one—i.e., tr(γe2)≈∑k=1∞nk2<1. Any occupation beyond a single NO is in the present context often called static correlation, which is equivalent to a nonzero generalized concurrence (20). However, in the Coulombic case, we cannot make the static correlation any larger.…”

Section: Equilibrium Long-range Correlationmentioning

confidence: 99%

Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry

Schäfer

Ruggenthaler

Appel

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

192

202

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Energy transfer in terms of excitation or charge is one of the most basic processes in nature, and understanding and controlling them is one of the major challenges of modern quantum chemistry. In this work, we highlight that these processes as well as other chemical properties can be drastically altered by modifying the vacuum fluctuations of the electromagnetic field in a cavity. By using a real-space formulation from first principles that keeps all of the electronic degrees of freedom in the model explicit and simulates changes in the environment by an effective photon mode, we can easily connect to well-known quantum-chemical results such as Dexter charge-transfer and Förster excitation-transfer reactions, taking into account the often-disregarded Coulomb and self-polarization interaction. We find that the photonic degrees of freedom introduce extra electron–electron correlations over large distances and that the coupling to the cavity can drastically alter the characteristic charge-transfer behavior and even selectively improve the efficiency. For excitation transfer, we find that the cavity renders the transfer more efficient, essentially distance-independent, and further different configurations of highest efficiency depending on the coherence times. For strong decoherence (short coherence times), the cavity frequency should be in between the isolated excitations of the donor and acceptor, while for weak decoherence (long coherence times), the cavity should enhance a mode that is close to resonance with either donor or acceptor. Our results highlight that changing the photonic environment can redefine chemical processes, rendering polaritonic chemistry a promising approach toward the control of chemical reactions.

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Section: Equilibrium Long-range Correlationmentioning

confidence: 99%

Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry

Schäfer

Ruggenthaler

Appel

et al. 2019

Proc. Natl. Acad. Sci. U.S.A.

192

202

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“…It is worthwhile mentioning that the CCR in equation (3.7) is a natural generalization of the complementarity relation obtained by Jakob & Bergou [52,53] for bipartite pure quantum systems. More generally, E = 2S l (ρ A 1 ), where E is the generalized concurrence obtained in [54] for multiparticle pure states. Now, for the boosted observer O' of §2, the same n massive quantons system is described by |Ψ Λ A 1 ,...,A 2n = U(Λ)|Ψ A 1 ,...,A 2n , and the density matrix of the multipartite pure quantum system can be written as [55,56]…”

Section: ⎛ ⎝mentioning

confidence: 99%

Complete complementarity relations and their Lorentz invariance

Basso

Maziero

2021

Proc. R. Soc. A.

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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. Peres et al. (Peres et al. 2002 Phys. Rev. Lett. 88 , 230402. ( doi:10.1103/PhysRevLett.88.230402 )) realized that even though it is possible to formally define spin in any Lorentz frame, there is no relationship between the observable expectation values in different Lorentz frames. Analogously, one can, in principle, define complementary relations in any Lorentz frame, but there is no obvious transformation law relating complementary relations in different frames. However, our result shows that the CCRs have the same value in any Lorentz frame, i.e. there is a transformation law connecting the CCRs. In addition, we explore relativistic scenarios for single and two-particle states, which helps in understanding the exchange of different aspects of a quantum system under Lorentz boosts.

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“…We consider that the system BCD has been measured in the computation basis states. The post measurement state vectors of system A can be represented as [2, 5]

χ_{0} = a false| 0 false〉 + p false| 1 false〉, χ_{1} = b false| 0 false〉 + q false| 1 false〉,

χ_{2} = c false| 0 false〉 + r false| 1 false〉, χ_{3} = d false| 0 false〉 + s false| 1 false〉,

χ_{4} = e false| 0 false〉 + t false| 1 false〉, χ_{5} = f false| 0 false〉 + u false| 1 false〉,

χ_{6} = g false| 0 false〉 + w false| 1 false〉, χ_{7} = h false| 0 false〉 + v false| 1 false〉 .

…”

Section: Preliminariesmentioning

confidence: 99%

“…introduced entropic entanglement measure [1]. A number of studies have been devoted to various measures of quantum entanglement in bipartite as well as multipartite settings [2–8]. Understanding the entanglement of a quantum system has become fundamental for the deeper understanding of quantum correlations as well as due to its immense applications in quantum computation and the information theory [9–11].…”

Section: Introductionmentioning

confidence: 99%

Geometry of distributive multiparty entanglement in 4 − qubit hypergraph states

Sarkar

Banerjee

Bag

et al. 2021

IET Quantum Communication

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A detailed investigation of the multiparty entanglement present in the 4 − qubit quantum hypergraph states is presented, following a measurement‐based geometrical approach. Considering a classification of the 4 − party quantum system represented by a mathematical hypergraph based on the connections between its vertices, the genuine 4 − party entanglement present in each bi‐partition of the states have been measured. A strong correlation between the connectivity of the vertices of the hypergraphs and the genuine 4 − party entanglement has been found. The equivalence of the genuine 4 − party entanglement present in each bi‐partition is shown considering similar connectivity of the vertices. This explicates the cyclic permutation symmetry of the multiparty entanglement present in the 4 − qubit hypergraph states. Physically, one may expect the quantum systems with superposition of many states to behave in this symmetric manner while mapped into a network‐type picture, which the authors have quantified, as well as classified in this work.

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Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange’s identity and wedge product

Cited by 41 publications

References 28 publications

Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry

Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry

Complete complementarity relations and their Lorentz invariance

Geometry of distributive multiparty entanglement in 4 − qubit hypergraph states

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