Monogamy Constraints Research Articles

Infrared gravity and a celestial obstruction to monogamy constraints

Infrared gravity and a celestial obstruction to monogamy constraints

Monogamy constraints on entanglement of four-qubit pure states

We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles, and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal state \(\rho \) of a four-qubit pure state \(\left| \Psi _{4}\right\rangle \), the non-Hermitian matrix \(\rho {\widetilde{\rho }}\) where \({\widetilde{\rho }}\) \(=\left( \sigma _{y} \otimes \sigma _{y}\right) \rho ^{*}\left( \sigma _{y}\otimes \sigma _{y}\right) \), contains information not only about the entanglement properties of the two-qubits in state \(\rho \) but also about three-tangles involving the selected pair as well as four-way correlations of the pair of qubits in \(\left| \Psi _{4}\right\rangle \). To extract information about tangles of a four-qubit state \(\left| \Psi _{4}\right\rangle \), the coefficients in the characteristic polynomial of matrix \(\rho {\widetilde{\rho }}\) are analytically expressed in terms of \(2\times 2\) matrices of state coefficients. Four-tangles distinguish between different types of entangled four-qubit pure states.

Tighter Monogamy Constraints in Multi-Qubit Entanglement Systems

We develop monogamy relations of multiqubit quantum entanglement in terms of the concurrence, entanglement of formation, convex-roof extended negativity and Tsallis-q entanglement. These monogamy inequalities are proved to be tighter than the existing ones. The corresponding examples are also presented.

Tripartite Einstein-Podolsky-Rosen steering with linear and nonlinear beamsplitters in four-wave mixing of Rubidium atoms.

Multipartite Einstein-Podolsky-Rosen (EPR) steering is an essential resource for secure one-sided device-independent quantum secret sharing. Here, we analyze the EPR steering properties exhibited in three-mode Gaussian states created by four-wave mixing (FWM) in Rubidium atoms combined with a linear beamsplitter and a nonlinear beamsplitter (second FWM), respectively. By quantifying Gaussian steerability based on a measure determined by the covariance matrix of the produced states, we compare the performance of two schemes to achieve one-way, collective, and genuine tripartite steering, as well as the monogamy constraints for distributing steering among three parties. We show that the scheme with nonlinear beamsplitter is feasible to create stronger bipartite steering and genuine tripartite steering and has more flexibility to manipulate the monogamy relation through the cooperation of the two cascaded FWM processes.

Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling

We present a phase control method for a general three-mode system with closed-loop coupling that drives the system into an entangled steady state and produces directional steering between two completely symmetric modes via quantum interference effects. In the scheme, two modes are coupled with each other both by a direct binary interaction and by an indirect interaction through a third intermediate damping mode, creating interference effects determined by the relative phase between the two physical interaction paths. By calculating the populations and correlations of the two modes, we show that, depending on the phase, two modes can be prepared into an entangled steady state with asymmetric and directional steering even if they possess completely symmetric decoherence properties. Meanwhile, entanglement and steering can be significantly enhanced due to constructive interference and thus are more robust to thermal noises. This provides an active method to manipulate the asymmetry of steering instead of adding asymmetric losses or noises to subsystems at the cost of reducing steerability. Moreover, we show that the interference effects can also enhance and control the correlations between other pairs of modes in the loop with opposite phase-dependent behavior, indicating monogamy constraints for distributing correlations among multiple parties. The present model could be applied in cavity optomechanical systems or in antiferromagnets where all components can mutually interact.

Multipartite Gaussian steering: Monogamy constraints and quantum cryptography applications

We derive laws for the distribution of quantum steering among different parties in multipartite Gaussian states under Gaussian measurements. We prove that a monogamy relation akin to the generalized Coffman-Kundu-Wootters inequality holds quantitatively for a recently introduced measure of Gaussian steering. We then define the residual Gaussian steering, stemming from the monogamy inequality, as an indicator of collective steering-type correlations. For pure three-mode Gaussian states, the residual acts a quantifier of genuine multipartite steering, and is interpreted operationally in terms of the guaranteed key rate in the task of secure quantum secret sharing. Optimal resource states for the latter protocol are identified, and their possible experimental implementation discussed. Our results pin down the role of multipartite steering for quantum communication.

Security proof for cryptographic protocols based only on the monogamy of Bell’s inequality violations

We show that monogamy of Bell's inequality violations, which is strictly weaker condition than no-signaling is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect no-signaling principle yet still allow for secure communication. This proves that no-signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results concerning the security of existing quantum key distribution protocols.

Bound of entanglement of assistance and monogamy constraints

We investigate the entanglement of assistance which quantifies capabilities of producing pure bipartite entangled states from a pure tripartite state. The lower bound and upper bound of entanglement of assistance are obtained. In the light of the upper bound, monogamy constraints are proved for arbitrary $n$-qubit states.

Correlation loss and multipartite entanglement across a black hole horizon (

We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.

Monogamy and ground-state entanglement in highly connected systems

We consider the ground-state entanglement in highly connected many-body systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their degree of connectivity, we investigate the interplay between the enhancement of entanglement, due to connections, and its frustration, due to monogamy constraints. Remarkably, we see that in many situations the degree of entanglement in a highly connected system is essentially of the same order as in a low connected one. We also identify instances in which the entanglement decreases as the degree of connectivity increases.

ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

Deterministic entanglement of assistance and monogamy constraints

Certain quantum-information tasks require entanglement of assistance, namely, a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that concurrence of assistance (COA) identifies capabilities of and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that COA is an entanglement monotone for $(2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}n)$-dimensional pure states. Moreover, if the COA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.

Revisiting Modernism with Kristeva: DeBeauvoir, Truffaut, and Renoir

Q WJimone DeBeauvoir's She Came to Stay {L'Invitee, 1943), Francois Truffauťs Jules and Jim (Jules et Jim, 1962) and Jean Renoir's The Rules of the Game (La Regle du jeu , 1939) examine the problem that monogamy poses for the female in mid-twentieth-century France.1 The heroine in each work (Francoise, Catherine, and Christine) tries to free herself from monogamy's constraints in an effort to give expression to the physical and emotional life threatened by her relationship to a man. The texts stage three different versions of a struggle to transform a dangerous monogamous relationship into a more open and satisfying one. Considering the texts in light of Julia Kristeva's reworking of Freud lays bare the psychological implications of these works. A re-interpretation in this light also demonstrates the validity and usefulness of her theory. Studying the male/female oppositions underlying personal and public relationships in these works reveals their critical reference to the collaboration with fascism in 1939 in France.