Is entanglement monogamous?

Abstract

We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy.We prove that if one can simulate these circuits classically efficiently then BQP ⊆ AM. and the National Reconnaissance Office. 1 Bernstein and Vazirani [BV97] proved that any model of quantum computation with measurements during the computation is no more powerful than a model with measurements at the end of the computation. Thus the rationale behind adaptive quantum computation is merely that the set of quantum gates that is needed to implement adaptive quantum computation may be smaller and therefore simpler to implement physically.

Entanglement switching via the Kondo effect in triple quantum dots

“…In Figure 3b forced to couple into a singlet, which can be considered as an example of the entanglement monogamy concept [56]. However, due to the substantial renormalization of the local moment S 2 C in the limit of small values, U/Γ < 4, the application of the pure spin model is not fully justified there.…”

Should Entanglement Measures be Monogamous or Faithful?

“…The study of entanglement and its distribution reveals fundamental insights into the nature of quantum correlations [3], on the properties of manybody systems [4,5], and on possibilities and limitations for quantum-enhanced technologies [6]. A particularly interesting feature of entanglement is known as monogamy [7], that is, the impossibility of sharing entanglement unconditionally across many subsystems of a composite quantum system.In the clearest manifestation of monogamy, if two parties A and B with the same (finite) Hilbert space dimension are maximally entangled, then their state is a pure state |Φ AB [8], and neither of them can share any correlation-let alone entanglement-with a third party C, as the only physically allowed pure states of the tripartite system ABC are product states |Φ AB ⊗ |Ψ C . Consider now the more realistic case of A and B being in a mixed, partially entangled state ρ AB .…”

“…, B n and such that the marginal state of A and any B j amounts to ρ AB . While even an entangled state can be shareable up to some number of extensions, a seminal result is that a state ρ AB is n-shareable for all n 2 if and only if it is separable, that is, no entangled state can be infinitely-shareable [7,[9][10][11][12]. This statement formalizes exactly the monogamy of entanglement (in an asymptotic setting), and has many important implications, including the equivalence between asymptotic quantum cloning and state estimation [13,14], the emergence of objectivity in the quantum-to-classical transition [15], the security of quantum key distribution [16][17][18][19], and the study of frustration and topological phases in many-body systems [20][21][22][23][24].…”

“…Any measure E is termed monogamous if, for all tripartite states, the ensuing entanglement distribution can be confined to a region strictly smaller than the white square with solid boundary. The latter denotes the trivial choice f (x, y) = max(x, y), which is satisfied a priori by any entanglement monotone E. a concept is monogamous in the n-shareability sense [7], one is led to raise the following key question: Should any valid entanglement measure be monogamous in a CKW-like sense?…”

“…The study of entanglement and its distribution reveals fundamental insights into the nature of quantum correlations [3], on the properties of manybody systems [4,5], and on possibilities and limitations for quantum-enhanced technologies [6]. A particularly interesting feature of entanglement is known as monogamy [7], that is, the impossibility of sharing entanglement unconditionally across many subsystems of a composite quantum system.…”