Random Dynamics

Bennett, D. L.; Brene, N.; Nielsen, Holger Bech

doi:10.1088/0031-8949/1987/t15/022

Cited by 13 publications

(19 citation statements)

References 12 publications

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“…This aspect seems to have a certain philosophical similarity with the random dynamics developed in[18], since any sophisticated discrete model would give some preferred symmetric states. There is a difference, however, since in our mechanism the model which is chosen will influence the symmetries which are highlighted, whereas random dynamics dictates that the specific model should not matter much for the emergent symmetries at large scales.…”

mentioning

confidence: 78%

“…To be more general one can look at general small perturbations around the symmetric configurations to make local statements. Let the tensor given in (17) be denoted by Q 0 and its corresponding action, (18), by S 0 . Ψ(Q) can be written, at least formally, for small perturbations Q = Q 0 + δQ as…”

Section: Perturbationsmentioning

confidence: 99%

“…For this, polar coordinates, where φ 1 = r cos(θ), φ 2 = r sin(θ), are most convenient since the critical points are degenerate along the angular direction. Plugging these coordinates into (18) gives a trivial integration over θ, removing the degeneracy. The remaining Gaussian integrals can be evaluated to be:…”

Section: Summary and Future Prospectsmentioning

confidence: 99%

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Symmetric configurations highlighted by collective quantum coherence

Obster

Sasakura

2017

Eur. Phys. J. C

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Recent developments in quantum gravity have shown the Lorentzian treatment to be a fruitful approach towards the emergence of macroscopic space-times. In this paper, we discuss another related aspect of the Lorentzian treatment: we argue that collective quantum coherence may provide a simple mechanism for highlighting symmetric configurations over generic non-symmetric ones. After presenting the general framework of the mechanism, we show the phenomenon in some concrete simple examples in the randomly connected tensor network, which is tightly related to a certain model of quantum gravity, i.e., the canonical tensor model. We find large peaks at configurations invariant under Lie-group symmetries as well as a preference for charge quantization, even in the Abelian case. In future study, this simple mechanism may provide a way to analyze the emergence of macroscopic space-times with global symmetries as well as various other symmetries existing in nature, which are usually postulated.

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confidence: 78%

Section: Perturbationsmentioning

confidence: 99%

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Symmetric configurations highlighted by collective quantum coherence

Obster

Sasakura

2017

Eur. Phys. J. C

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“…The first defect may be remedied by combining a random graph model with a gauge model to form a kind of gauge glass (Bennet et al, 1987), but to cure the second we must go further.…”

Section: Gauge Symmetry and Matrix Modelsmentioning

confidence: 99%

Principle of event symmetry

Gibbs

1996

Int J Theor Phys

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To accommodate topology change, the symmetry of space-time must be extended from the diffeomorphism group of a manifold to the symmetric group acting on the discrete set of space-time events. This is the principle of event-symmetric space-time. I investigate a number of physical toy models with this symmetry to gain some insight into the likely nature of event-symmetric space-time, In the more advanced models the symmetric group is embedded into larger structures such as matrix groups which provide scope to unify space-time symmetry with the internal gauge symmetries of particle physics, I also suggest that the symmetric group of space-time could be related to the symmetric group acting to exchange identical particles, implying a unification of space-time and matter. I end with a definition of a new type of loop symmetry which is important in event-symmetric superstring theory.

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“…Quantum entanglement [1], one of the most striking features in quantum mechanics, is the essential resource [2] for a plethora of quantum information protocols like quantum teleportation [3], quantum dense coding [4], entanglement-based quantum cryptography [5], one-way quantum computation [6] etc. These protocols revolutionize the existing communication and computation schemes based on laws of classical mechanics.…”

Section: Introducionmentioning

confidence: 99%

Universality in distribution of monogamy scores for random multiqubit pure states

et al. 2019

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Monogamy of quantum correlations provides a way to study restrictions on their sharability in multiparty systems. We find the critical exponent of these measures, above which randomly generated multiparty pure states satisfy the usual monogamy relation, and show that the critical power decreases with the increase in the number of parties. For three-qubit pure states, we detect that W-class states are more prone to being nonmonogamous as compared to the GHZ-class states. We also observe a different criticality in monogamy power up to which random pure states remain nonmonogamous. We prove that the "average monogamy" score asymptotically approaches its maximal value on increasing the number of parties. Analyzing the monogamy scores of random three-, four-, five-and six-qubit pure states, we also report that almost all random pure six-qubit states possess maximal monogamy score, which we confirm by evaluating statistical quantities like mean, variance and skewness of the distributions. In particular, with the variation of number of qubits, means of the distributions of monogamy scores for random pure states approach to unitywhich is the algebraic maximum -thereby conforming to the known results of random states having maximal multipartite entanglement in terms of geometric measures. I. INTRODUCIONQuantum entanglement [1], one of the most striking features in quantum mechanics, is the essential resource [2] for a plethora of quantum information protocols like quantum teleportation [3], quantum dense coding [4], entanglement-based quantum cryptography [5], one-way quantum computation [6] etc. These protocols revolutionize the existing communication and computation schemes based on laws of classical mechanics. Due to immense importance of entanglement, over the years, several detection methods like partial transposition [7] based on positive maps [8], entanglement witness, [9][10][11], and quantifiers such as distillable entanglement [12], entanglement of formation [13,14], logarithmic negativity [15,16] have been proposed. On the other hand, it has also been realized that quantum mechanical systems can exhibit nonclassical phenomena which cannot be explained by using the theory of entanglement, and hence a different resource theory has been developed where unlike separable states, "classically correlated" states in the computational basis are the free states [17]. These measures, independent of entanglement, belonging to a finegrained paradigm of quantum correlations (QC), have their origin in the concepts of information theory or geometry of states or thermodynamics. Examples of such measures include quantum discord [18], geometric quantum discord [19], quantum work deficit [20,21], and quantum deficit [22] (see review [17]).Beyond the bipartite domain, understanding of QC, even for pure states shared by multiple parties, is limited due to its complex structure. In this paper, we study the distribution of QC among the various parties of a random multipartite quantum state, with the help of the concept of "monogamy" [...

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Random Dynamics

Cited by 13 publications

References 12 publications

Symmetric configurations highlighted by collective quantum coherence

Symmetric configurations highlighted by collective quantum coherence

Principle of event symmetry

Universality in distribution of monogamy scores for random multiqubit pure states

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