Tripartite Systems Research Articles

Monogamy of Einstein‐Podolsky‐Rosen Steering in the Background of an Asymptotically Flat Black Hole

AbstractWe study the behavior of monogamy deficit and monogamy asymmetry for Einstein‐Podolsky‐Rosen steering of Gaussian states under the influence of the Hawking effect. We demonstrate that the monogamy of quantum steering shows an extreme scenario in the curved spacetime: the first part of a tripartite system cannot individually steer two other parties, but it can steer the collectivity of the remaining two parties. We also find that the monogamy deficit of Gaussian steering, a quantifier of genuine tripartite steering, are generated due to the influence of the Hawking thermal bath. Our results elucidate the structure of quantum steering in tripartite quantum systems in curved spacetime.

Measure and detection of genuine multipartite entanglement for tripartite systems

It is a computationally hard task to certify genuine multipartite entanglement (GME). We investigate the relation between the norms of the correlation vectors and the detection of GME for tripartite quantum systems. A sufficient condition for GME and an effective lower bound for the GME concurrence are derived. Several examples are considered to show the effectiveness of the criterion and the lower bound of GME concurrence.

Revealing Tripartite Quantum Discord with Tripartite Information Diagram

A new measure based on the tripartite information diagram is proposed for identifying quantum discord in tripartite systems. The proposed measure generalizes the mutual information underlying discord from bipartite to tripartite systems, and utilizes both one-particle and two-particle projective measurements to reveal the characteristics of the tripartite quantum discord. The feasibility of the proposed measure is demonstrated by evaluating the tripartite quantum discord for systems with states close to Greenberger–Horne–Zeilinger, W, and biseparable states. In addition, the connections between tripartite quantum discord and two other quantum correlations—namely genuine tripartite entanglement and genuine tripartite Einstein–Podolsky–Rosen steering—are briefly discussed. The present study considers the case of quantum discord in tripartite systems. However, the proposed framework can be readily extended to general N-partite systems.

Multipartite analysis of average-subsystem entropies

So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average subsystem entropies. These quantities are standard tools in quantum information theory, most typically applied in bipartite systems. We shall first present some extensions to the usual bipartite analysis, (including a calculation of the average tangle, and a bound on the average concurrence), follow this with some useful results for tripartite systems, and finally extend the discussion to arbitrary multi-partite systems. A particularly nice feature of tri-partite and multi-partite analyses is that this framework allows one to introduce an "environment" for small subsystems to couple to.

Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in Multipartite Systems

We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover,two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased.

Tensor network models of unitary black hole evaporation

We introduce a general class of toy models to study the quantum information-theoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a tensor product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a tensor network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final tensor product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the “information-free” property of black hole horizons are those whose isometries are tensors corresponding to states of tripartite systems with maximally mixed subsystems.

Page curves for tripartite systems

We investigate information flow and Page curves for tripartite systems. We prepare a tripartite system (say, A, B, and C) of a given number of states and calculate information and entropy contents by assuming random states. Initially, every particle was in A (this means a black hole), and as time goes on, particles move to either B (this means Hawking radiation) or C (this means a broadly defined remnant, including a non-local transport of information, the last burst, an interior large volume, or a bubble universe, etc). If the final number of states of the remnant is smaller than that of Hawking radiation, then information will be stored by both the radiation and the mutual information between the radiation and the remnant, while the remnant itself does not contain information. On the other hand, if the final number of states of the remnant is greater than that of Hawking radiation, then the radiation contains negligible information, while the remnant and the mutual information between the radiation and the remnant contain information. Unless the number of states of the remnant is large enough compared to the entropy of the black hole, Hawking radiation must contain information; and we meet the menace of black hole complementarity again. Therefore, this contrasts the tension between various assumptions and candidates of the resolution of the information loss problem.

Entanglement of two hybrid optomechanical cavities composed of BEC atoms under Bell detection

In this paper, firstly, we consider bipartite entanglement between each part of an optomechanical cavity composed of one dimensional Bose-Einstein condensate (BEC). we investigate atomic collision on the behavior of the BEC in the week photon-atom coupling constant, and use Bogoliubov approximation for the BEC. Secondly under above condition, we propose a scheme for entanglement swapping protocol wich involves tripartite systems. In our investigation, we consider a scenario where BECs, moving mirrors, and optical cavity modes are given in a Gaussian state with a covariance matrix (CM). By applying the Bell measurment to the output optical field modes, we show how the remote entanglement between two BECs, two moving mirrors, and BEC-mirror modes in different optomechanical cavity can be generated.

Exploring Tripartite Quantum Correlations: Entanglement Witness and Quantum Discord

In this study, we explore the tripartite quantum correlations by employing the quantum relative entropy as a distance measure. First, we evaluate the explicit expression for nonlinear entanglement witness (EW) of tripartite systems in the four dimensional space that lends itself to a straightforward algorithm for finding closest separable state (CSS) to the generic state. Then using nonlinear EW with specific feasible regions (FRs), quantum discord is derived analytically for the three-qubit and tripartite systems in the four dimensional space. Furthermore, we explicitly figure out the additivity relation of quantum correlations in tripartite systems.

The local indistinguishability of multipartite product states

We study the perfectly local indistinguishability of multipartite product states. Firstly, we follow the method of Zhang et al. (Phys Rev A 93:012314, 2016) to give another more concise set of $$2n-1$$ orthogonal product states in $${\mathbb {C}}^m\otimes {\mathbb {C}}^n$$ $$(4\le m\le n)$$ which can not be distinguished by local operations and classical communication. Then we use the three-dimensional cubes to present some product states which give us an intuitive view on how to construct locally indistinguishable product states in tripartite quantum systems. At last, we give an explicit construction of locally indistinguishable orthogonal product states for general multipartite systems.

Some applications of uncertainty relations in quantum information

We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the Einstein, Podolsky and Rosen (EPR) paradox. Entropic uncertainty relations (EURs) are used to reveal quantum steering for non-Gaussian continuous variable states. EURs for discrete variables are studied in the context of quantum memory where fine-graining yields the optimum lower bound of uncertainty. The fine-grained uncertainty relation is used to obtain connections between uncertainty and the nonlocality of retrieval games for bipartite and tripartite systems. The Robertson-Schrödinger (RS) uncertainty relation is applied for distinguishing pure and mixed states of discrete variables.

Coherence Trade-off relations in Multipartite systems

Quantum coherence is investigated using a new measure with metric properties and entropic nature and decomposed into local and intrinsic contributions. The trade-off relation between these contributions as well as their distribution properties are studied for simple tripartite systems and the more complex spin chain model. We find that the coherence changes its nature with respect to the parameters of the quantum state under investigation.

Agreement attraction in Serbian

Asymmetric number attraction effects have been typically explained via a privative markedness account: plural nouns are more marked than singular ones and thus stronger attractors. However, this account does not explain results from tripartite systems, in which a third number value is available, like paucal. Here we tested whether attraction effects can be driven by specific markedness sub-components, such as frequency/naturalness of use, using Serbian, in which participles can agree with masculine subjects in singular, plural and paucal. We first conducted a naturalness judgment task, finding the following naturalness/frequency pattern: singular,plural<paucal. In a subsequent forced-choice task, we presented participants with preambles containing a singular, a plural or a paucal headnoun (the castle[Sg] /two castles[Pauc] /the castles[Pl]) modified by singular/plural/paucal attractors (with the window[Sg] /with two windows[Pauc] /with the windows[Pl]). Three options were provided to complete the sentence (resembles[Sg] /resemble[Pauc] /resemble[Pl] gothic architecture).Both accuracy and reaction times (RTs) were collected. Accuracy data reflected the naturalness/frequency pattern, with paucal being the strongest attractor, and plural and singular attracting equally. However, reaction times showed a difference between singular and plural, suggesting co-influence of both frequency/naturalness and morphological markedness. We emphasize the necessity of re-defining markedness and testing attraction through different markedness sub-components (i.e. frequency/naturalness) to explain attraction cross-linguistically.

Versatility of continuous-variable asymmetric tripartite entanglement allows Alice and Clare to keep secrets from Bob

The fully symmetric Gaussian tripartite entangled pure states will not exhibit two-mode Einstein Podolsky-Rosen (EPR)-steering. This means that any two participants cannot share quantum secrets using the security of one-sided device independent quantum key distribution (1SDI-QKD) without involving the third. They are restricted at most to standard quantum key distribution (S-QKD), which is less secure. Here we show that least some asymmetric tripartite systems can exhibit bipartite EPR-steering, so that two of the participants can use 1SDI-QKD without involving the other. This is possible because the promiscuity relations of continuous-variable tripartite entanglement are different from those of discrete-variable systems. We analyse these properties for two different systems, showing that the asymmetric system has an extra degree of flexibility not found in the symmetric one.

Lower bound on concurrence for arbitrary-dimensional tripartite quantum states

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.

Bipartite entanglement in continuous-variable tripartite systems

In the field of continuous-variable tripartite entanglement, the systems utilised can be either asymmetric or symmetric. It is therefore of interest to examine the differences in the entanglement properties of these two types of system, using two examples that are known to produce tripartite entanglement. We examine one asymmetric and one fully symmetric Gaussian continuous-variable system in terms of their tripartite and bipartite entanglement properties. We first treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models. Our symmetric system exhibits perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, the two systems exhibit both tripartite and bipartite entanglement. Secondly we treat the more experimentally reasonable situation where the interactions take place inside optical cavities and we are dealing with mixed states. In these cases, where the criteria for genuine tripartite entanglement are more stringent, we find that tripartite entanglement is still available, although over smaller bandwidths than three-mode inseparability. In general, the spectral results are consistent with the analytical solutions. We conclude that none of the outputs are completely analogous to either GHZ or W states, but there are parameter regions of the Hamiltonian dynamics where they produce T states as introduced by Adesso et al. [1,2]. In the intracavity cases, both bipartite entanglement and tripartite inseparability are always present, with genuine tripartite entanglement appearing as the pumping rate is increased. The qualitative differences in the output states for different interaction parameters indicate that continuous-variable tripartite quantum information systems offer a versatility not found in two-mode bipartite systems.

Subadditivity and Strong Subadditivity Conditions for the Density Matrix of the Five-Level Atom

We obtain new quantum inequalities for von Neumann entropy of the five-level atom, which are analogs of the subadditivity condition known for bipartite quantum systems and the strong subadditivity condition known for tripartite quantum systems. We discuss the possibility to check the inequalities for the single qudit with j = 2, which can be realized as a five-level atom in the experiments with superconducting circuits. We present the strong subadditivity conditions for the finite-level atomic populations.

Keeping the Wolves at Bay: Antitoxins of Prokaryotic Type II Toxin-Antitoxin Systems.

In their initial stages of discovery, prokaryotic toxin-antitoxin (TA) systems were confined to bacterial plasmids where they function to mediate the maintenance and stability of usually low- to medium-copy number plasmids through the post-segregational killing of any plasmid-free daughter cells that developed. Their eventual discovery as nearly ubiquitous and repetitive elements in bacterial chromosomes led to a wealth of knowledge and scientific debate as to their diversity and functionality in the prokaryotic lifestyle. Currently categorized into six different types designated types I–VI, type II TA systems are the best characterized. These generally comprised of two genes encoding a proteic toxin and its corresponding proteic antitoxin, respectively. Under normal growth conditions, the stable toxin is prevented from exerting its lethal effect through tight binding with the less stable antitoxin partner, forming a non-lethal TA protein complex. Besides binding with its cognate toxin, the antitoxin also plays a role in regulating the expression of the type II TA operon by binding to the operator site, thereby repressing transcription from the TA promoter. In most cases, full repression is observed in the presence of the TA complex as binding of the toxin enhances the DNA binding capability of the antitoxin. TA systems have been implicated in a gamut of prokaryotic cellular functions such as being mediators of programmed cell death as well as persistence or dormancy, biofilm formation, as defensive weapons against bacteriophage infections and as virulence factors in pathogenic bacteria. It is thus apparent that these antitoxins, as DNA-binding proteins, play an essential role in modulating the prokaryotic lifestyle whilst at the same time preventing the lethal action of the toxins under normal growth conditions, i.e., keeping the proverbial wolves at bay. In this review, we will cover the diversity and characteristics of various type II TA antitoxins. We shall also look into some interesting deviations from the canonical type II TA systems such as tripartite TA systems where the regulatory role is played by a third party protein and not the antitoxin, and a unique TA system encoding a single protein with both toxin as well as antitoxin domains.

Variability of ecological and autotrophic host specificity in a mycoheterotrophic system: Pterospora andromedea and associated fungal and conifer hosts

Abstract Few studies of tripartite mycoheterotrophic systems have examined ecological specificity across broad geographic ranges or addressed autotrophic host specificity. Pterospora andromedea was selected as an ideal candidate to examine ecological specificity of a mycoheterotrophic system as it is widely distributed, has been shown to have high levels of symbiont specificity with Rhizopogon subgenus Amylopogon , and is found with several autotrophic hosts. Pairs of P. andromedea + Rhizopogon spp. samples were co-collected across North America and were sequenced using trnL and ITS, respectively. Bayesian phylogenetic reconstructions between the co-collected taxa were used to examine ecological specificity, and for subsequent tests for autotroph specificity. P. andromedea lineages exhibited both high specificity and relaxed specificity for fungal symbionts and autotrophic hosts across the geographic landscape under allopatric and sympatric conditions. This strong evidence for geographic mosaics of specificity in mycoheterotrophic systems is an important future consideration in determining the evolutionary ecology of mycoheterotrophs.

Quantum correlations between each two-level system in a pair of atoms and general coherent fields

The quantitative description of the quantum correlations between each two-level system in a two-atom system and the coherent fields initially defined in a coherent state in the framework of power-law potentials (PLPCSs) is considered. Specifically, we consider two atoms locally interacting with PLPCSs and take into account the different terms of interactions, the entanglement and quantum discord are studied including the time-dependent coupling and photon transition effects. Using the monogamic relation between the entanglement of formation and quantum discord in tripartite systems, we show that the control and preservation of the different kinds of quantum correlations greatly benefit from the combination of the choice of the physical quantities. Finally, we explore the link between the dynamical behavior of quantum correlations and nonclassicality of the fields with and without atomic motion effect.