Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster state model, and it was hence believed that with this approach many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as "computationally universal" states--i.e. they allow one to efficiently reproduce the classical output of each quantum computation--whereas the cluster states are universal in a stronger sense since they are "universal state preparators". Here we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.
In this paper, we discuss extremal extensions of entanglement witnesses based on Choi's map. The constructions are based on a generalization of the Choi map due to Osaka, from which we construct entanglement witnesses. These extremal extensions are powerful in terms of their capacity to detect entanglement of positive under partial transpose (PPT) entangled states and lead to unearthing of entanglement of new PPT states. We also use the Cholesky-like decomposition to construct entangled states which are revealed by these extremal entanglement witnesses.
We establish a novel procedure to analyze the entanglement properties of extremal density matrices depending on the parameters of a finite dimensional Hamiltonian. It was applied to a general 2-qubit Hamiltonian which could exhibit Kramers degeneracy. This is done through the extremal density matrix formalism, which allows to extend the conventional variational principle to mixed states. By applying the positive partial transpose criterion in terms of the Correlation and Schlienz-Mahler matrices on the extremal density matrices, we demonstrate that it is possible to reach both pure and mixed e…
In this paper we describe a new connection between UPB (unextendable product bases) and P (positive) maps which are not CP (completely positive). We show that inner automorphisms of the set of P maps which are not CP, produce extremal extensions of these maps that help in entanglement detection. By constructing such an extension of the well-known Choi map, we strengthen its power to unearth PPT (positive under partial transpose) entangled states. We further show that the class of maps generated from the Choi map via an inner automorphism naturally detects the entanglement of states in the orth…
We define an entanglement witness in a composite quantum system as an observable having nonnegative expectation value in every separable state. Then a state is entangled if and only if it has a negative expectation value of some entanglement witness. Equivalent representations of entanglement witnesses are as nonnegative biquadratic forms or as positive linear maps of Hermitian matrices. As reported elsewhere, we have studied extremal entanglement witnesses in dimension $3\times 3$ by constructing numerical examples of generic extremal nonnegative forms. These are so complicated that we do not…
We study extremal entanglement witnesses on a bipartite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus $\textrm{Tr}\,Ωρ\geq 0$ when $Ω$ is a witness and $ρ$ a pure product state, $ρ=ψψ^{\dagger}$ with $ψ=ϕ\otimesχ$. The set of witnesses of unit trace is a compact convex set, defined by its extremal points. The expectation value $f(ϕ,χ)=\mathrm{Tr}\,Ωρ$ as a function of $ϕ$ and $χ$ is a nonnegative biquadratic form. Every zero of $f(ϕ,χ)$ imposes real-linear constraints on $f$ and $Ω$. The Hessian matrix at the zero must be nonnegative…
Quantum entanglement as an extremal Kirkwood-Dirac nonreality
Research Center for Quantum Physics, National Research and Innovation Agency（量子物理研究中心，国家研究与创新局）；Research Center for Nanoscience and Nanotechnology, Bandung Institute of Technology（纳米科学与纳米技术中心，万隆理工学院）；Department of Engineering Physics, Bandung Institute of Technology（工程物理系，万隆理工学院）
Unlike bosons, fermions always have a non-trivial entanglement. Intuitively, Slater determinantal states should be the least entangled states. To make this intuition precise we investigate entropy and entanglement of fermionic states and prove some extremal and near extremal properties of reduced density matrices of Slater determinantal states.
We study state engineering through bilinear interactions between two remote qubits and two-mode Gaussian light fields. The attainable two-qubit states span the entire physically allowed region in the entanglement-versus-global-purity plane. Two-mode Gaussian states with maximal entanglement at fixed global and marginal entropies produce maximally entangled two-qubit states in the corresponding entropic diagram. We show that a small set of parameters characterizing extremally entangled two-mode Gaussian states is sufficient to control the engineering of extremally entangled two-qubit states, wh…
We give an explicit family of XOR games with O(n)-bit questions requiring 2^n ebits to play near-optimally. More generally we introduce a new technique for proving lower bounds on the amount of entanglement required by an XOR game: we show that near-optimal strategies for an XOR game G correspond to approximate representations of a certain C^*-algebra associated to G. Our results extend an earlier theorem of Tsirelson characterising the set of quantum strategies which implement extremal quantum correlations.
It is nowadays accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a quantum state from entangled to separable and vice versa. We propose to certify the presence of quantumness via an average over all physically relevant modal decompositions. We investigate extremal states for such a measure: SU(2)-coherent states possess the least quantumness whereas the opposite extreme is inhabited by states with maximally spread Majorana constellations.
We investigate the $Λ$-polytopes, a convex-linear structure recently defined and applied to the classical simulation of quantum computation with magic states by sampling. There is one such polytope, $Λ_n$, for every number $n$ of qubits. We establish two properties of the family $\{Λ_n, n\in \mathbb{N}\}$, namely (i) Any extremal point (vertex) $A_α\in Λ_m$ can be used to construct vertices in $Λ_n$, for all $n>m$. (ii) For vertices obtained through this mapping, the classical simulation of quantum computation with magic states can be efficiently reduced to the classical simulation based on th…
Timing quantum emission: Coherence, superradiance, and entanglement in order
University of Otago（奥塔哥大学）；National University of Singapore（新加坡国立大学）；University of Sydney（悉尼大学）；Carl von Ossietzky University Oldenburg（奥尔登堡卡尔·冯·奥西茨基大学）；Nanyang Technological University（南洋理工大学）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
Institute of Theoretical Physics, University of Wrocław（弗罗茨瓦夫大学理论物理研究所）；Institute of Theoretical Physics, Faculty of Physics, University of Warsaw（华沙大学物理学院理论物理研究所）
One of the most fundamental questions in quantum information theory is PPT-entanglement of quantum states, which is an NP-hard problem in general. In this paper, however, we prove that all PPT $(\overlineπ_A\otimes π_B)$-invariant quantum states are separable if and only if all extremal unital positive $(π_B,π_A)$-covariant maps are decomposable where $π_A,π_B$ are unitary representations of a compact group and $π_A$ is irreducible. Moreover, an extremal unital positive $(π_B,π_A)$-covariant map $\mathcal{L}$ is decomposable if and only if $\mathcal{L}$ is completely positive or completely cop…
The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.
In this paper we describe the structure of extremal stationary spherically symmetric black hole solutions in the STU model of D=4, N=2 supergravity in terms of four-qubit systems. Our analysis extends the results of previous investigations based on three qubits. The basic idea facilitating this four-qubit interpretation is the fact that stationary solutions in D=4 supergravity can be described by dimensional reduction along the time direction. In this D=3 picture the global symmetry group $SL(2,R)^{\times 3}$ of the model is extended by the Ehlers SL(2,R) accounting for the fourth qubit. We in…
The quantum vacuum has long been known to be characterized by field correlations between spacetime points. These correlations can be swapped with a pair of particle detectors, modelled as simple two-level quantum systems (Unruh-DeWitt detectors) via a process known as entanglement harvesting. We study this phenomenon in the presence of a rotating BTZ black hole, and find that rotation can significantly amplify the harvested vacuum entanglement. Concurrence between co-rotating detectors is amplified by as much as an order of magnitude at intermediate distances from the black hole relative to th…
The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we derive its closed expression for relevant two-qubit states. We study its analytical relation w…
