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Laser Physics

Decay of negativity of randomized multiqubit mixed states

Mostafa Mansour, Y. Oulouda, A. Sbiri, Mohammed El Falaki

Published Feb 9, 2021• 18 citations
Publisher

Abstract

Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .

DOI
10.1088/1555-6611/abdeca

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Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .
Randomized measurements constitute a simple measurement primitive that exploits the information encoded in the outcome statistics of samples of local quantum measurements defined through randomly selected bases. In this work we exploit the potential of randomized measurements in order to probe the amount of entanglement contained in multiparticle quantum systems as quantified by the multiparticle concurrence. We further present a detailed statistical analysis of the underlying measurement resources required for a confident estimation of the introduced quantifiers using analytical tools from the theory of random matrices. The introduced framework is demonstrated by a series of numerical experiments analyzing the concurrence of typical multiparticle entangled states as well as of ensembles of output states produced by random quantum circuits. Finally, we examine the multiparticle entanglement of mixed states produced by noisy quantum circuits consisting of single- and two-qubit gates with nonvanishing depolarization errors, thus showing that our framework is directly applicable in the noisy intermediate-scale regime.
Based on quantum complementary relations (QCRs) and a purification scenario, we analyze a class of NNN-qubit mixed states that are entangled but do not have two-, and genuine three-, four-,\dots{},NNN-qubit entanglements. It is shown that entanglement (one-tangle or negativity) in these mixed states is closely related to the QCR entanglement of their purified states. In particular, it is elaborated that when the mixed state does not have multipartite tangles (two- and higher tangles), its entanglement is actually a kind of genuine multipartite QCR entanglement between the system and its environment.
We investigate the decoherence of maximally mixed multi-partite cluster states of a physical system of n qubits. We introduce the disconnected cluster states for an ensemble of non interacting qubits and we give the corresponding separable density matrices. The maximally entangled cluster states can be generated from disconnected cluster states, by applying the entanglig operators between the pair of qubits. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled cluster state to a decohered mixed state. The deco-hered mixed states for multipartite systems are explicitly expressed and their bipartite entanglement is characterized by using the genuine multipartite neg-ativity as a quantifier of entanglement. Conclusion Entangled cluster states are obtained by a dynamical evolution of multi-qubit system by using an Hamiltonian of Ising type. Cluster states are of great interest in quantum computing and are suitable in various tasks of quantum computation. Decohered mixed states are derived via a local noisy evolution of the entangled multi-qubit system in contact with environment. More precisely , under the influence of the de-coherence, the multi-qubit system loses entanglement and evolves from it's initial maximally entangled cluster state to a decohered mixed state. More precisely we have given explicit expressions of decohered mixed states derived from n-qubit entangled cluster states. The separability for decohered mixed states is addressed with the concept of the genuine multipartite nega-tivity.
Random quantum states serve as a powerful tool in various scientific fields, including quantum supremacy and black hole physics. It has been theoretically predicted that entanglement transitions may happen for different partitions of multipartite random quantum states; however, the experimental observation of these transitions is still absent. Here, we experimentally demonstrate the entanglement transitions witnessed by negativity on a fully connected superconducting processor. We apply parallel entangling operations, that significantly decrease the depth of the pseudo-random circuits, to generate pseudo-random pure states of up to 15 qubits. By quantum state tomography of the reduced density matrix of six qubits, we measure the negativity spectra. Then, by changing the sizes of the environment and subsystems, we observe the entanglement transitions that are directly identified by logarithmic entanglement negativities based on the negativity spectra. In addition, we characterize the randomness of our circuits by measuring the distance between the distribution of output bit-string probabilities and the Porter-Thomas distribution. Our results show that superconducting processors with all-to-all connectivity constitute a promising platform for generating random states and understanding the entanglement structure of multipartite quantum systems.
We present an approach to the study of entanglement decay which focuses on collective properties. As an example, we investigate the entanglement decay of a two-qubit system produced by local identical reservoirs acting on the qubits for three experimentally and theoretically relevant cases. We study the probability distributions of disentanglement times, a quantity independent of the measure used to quantify entanglement, and the time-dependent probability distribution of concurrence. Analytical results are obtained for initially uniformly distributed pure states. The calculation of these probability distributions gives a complete insight into how different decoherence channels affect the entanglement initially contained in the set of two-qubit pure states. Numerical results are reported for randomly distributed initial mixed states. Although the paper focuses in Markovian noisy channels, we show that our results also describe nonautonomous and non-Markovian channels.