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Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to quenched disorder

George Biswas, Anindya Biswas, Ujjwal Sen

Published May 7, 2021• 0 citations
OpenAlex

Abstract

The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response of quenched disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, quenched averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and for disorder insertions in one and several state parameters. The non-Gaussian distributions considered are uniform and Cauchy-Lorentz. Two- and three-qubit pure state Haar-uniform generations are considered for the typical state productions. We also consider noisy versions of the initial states produced in the Haar-uniform generations. A genuine multiparty entanglement monotone is considered for the three-qubit case, while concurrence is used to measure two-qubit entanglement.

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The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response of quenched disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, quenched averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and for disorder insertions in one and several state parameters. The non-Gaussian distributions considered are uniform and Cauchy-Lorentz. Two- and three-qubit pure state Haar-uniform generations are considered for the typical state productions. We also consider noisy versions of the initial states produced in the Haar-uniform generations. A genuine multiparty entanglement monotone is considered for the three-qubit case, while concurrence is used to measure two-qubit entanglement.
Abstract The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response to disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and for disorder insertions in one and several state parameters. The non-Gaussian distributions considered are uniform and Cauchy–Lorentz. Two- and three-qubit pure state Haar-uniform generations are considered for the typical state productions. We also consider noisy versions of the initial states produced in the Haar-uniform generations. A genuine multiparty entanglement monotone is considered for the three-qubit case, while concurrence is used to measure two-qubit entanglement.
Abstract We consider the average quantum coherences of typical redits and qudits—vectors of real and complex Hilbert spaces—with the analytical forms stemming from the symmetry of Haar-uniformly distributed random pure states. We subsequently study the response to disorder in spread of the typical quantum coherence in response to glassy disorder. The disorder is inserted in the state parameters. Even in the absence of disorder, the quantum coherence distributions of redits and qudits are not uniform over the range of quantum coherence, and the spreads are relatively lower for higher dimensions. On insertion of disorder, the spreads decrease. This decrease in the spread of quantum coherence distribution in response to disorder is seen to be a generic feature of typical pure states: we observe the feature for different strengths of disorder and for various types of disorder distributions, viz. Gaussian, uniform, and Cauchy–Lorentz. We also find that the quantum coherence distributions become less asymmetric with increase in dimension and with infusion of glassy disorder.
Abstract We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots exhibit non-uniform distributions. The distribution depends on the entanglement of the fixed reference quantum state used to quantify the fidelity of the random pure bipartite states. We find that the average fidelity of typical random pure bipartite qubits within a narrow entanglement range with respect to a randomly chosen fixed bipartite qubit is 1 4 . Extending our study to higher dimensional bipartite qudits, we find that the average fidelity of typical random pure bipartite qudits with respect to a randomly chosen fixed bipartite qudit remains constant within a narrow entanglement range. The values of these constants are 1 d 2 , with d being the dimension of the local Hilbert space of the bipartite qudit system, suggesting a consistent relationship between entanglement and fidelity across different dimensions. The probability distribution functions of fidelity with respect to a product state are analytically studied and used as a reference for the benchmarking of distributed quantum computing devices.
Trends of genuine entanglement in Haar uniformly generated multimode pure Gaussian states with fixed average energy per mode are explored. A distance-based metric known as the generalized geometric measure (GGM) is used to quantify genuine entanglement. The GGM of a state is defined as its minimum distance from the set of all non-genuinely entangled states. To begin with, we derive an expression for the Haar averaged value of any function defined on the set of energy-constrained states. Subsequently, we investigate states with a large number of modes and provide a closed-form expression for the Haar averaged GGM in terms of the average energy per mode. Furthermore, we demonstrate that typical states closely approximate their Haar averaged GGM value, with deviation probabilities bounded by an exponentially suppressed limit. We then analyze the GGM content of typical states with a finite number of modes and present the distribution of GGM. Our findings indicate that as the number of modes increases, the distribution shifts towards higher entanglement values and becomes more concentrated. We quantify these features by computing the Haar averaged GGM and the standard deviation of the GGM distribution, revealing that the former increases while the latter decreases with the number of modes.
We investigate multipartite entanglement via the statistical properties of pure quantum states of n-qubits. By analyzing the distribution of purity among balanced bipartitions, we compare Haar-typical states, uniformly distributed on the unit sphere of states, with Hadamard states, being characterized by equal weights in the computational basis. We analyze different ensembles of Hadamard states characterized by their phase distributions. Through analytical and numerical calculations, we show that Hadamard states exhibit, on average, a higher degree of entanglement than Haar-typical states. In addition, we show that a particular class of Hadamard states, characterized by real coefficients with alternating signs, known as hypergraph states, appears especially relevant in the search for maximally multipartite entangled states, both for their structural simplicity and the increased likelihood of sampling highly entangled states. These results identify Hadamard states as a tractable yet promising class for exploring multipartite entanglement structures and advancing the characterization of maximally multipartite entangled quantum states.
We investigate the patterns in distributions of localizable entanglement over a pair of qubits for random multiqubit pure states. We observe that the mean of localizable entanglement increases gradually with increasing the number of qubits of random pure states while the standard deviation of the distribution decreases. The effects on the distributions, when the random pure multiqubit states are subjected to local as well as global noisy channels, are also investigated. Unlike the noiseless scenario, the average value of the localizable entanglement remains almost constant with the increase in the number of parties for a fixed value of noise parameter. We also find that the maximum strength of noise under which entanglement survives can be independent of the localizable entanglement content of the initial random pure states.