Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer

Gårding, Elias Riedel; Schwaller, Nicolas; Chan, Chun Lam; Chang, Su Yeon; Bosch, Samuel; Gessler, Frédéric; Laborde, Willy Robert; Hernández, Javier Naya; Si, Xinyu; Dupertuis, M.‐A.; Macris, Nicolas

doi:10.3390/e23070797

Cited by 15 publications

(17 citation statements)

References 55 publications

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“…A statistical mixture of these pure quantum states is called a BDS. Despite their simple structure, BDSs play a crucial role in the theory of quantum information [34], because they form a representative three-dimensional subspace of the full 15-dimensional space of two-qubit mixed states. The two-qubit state is a BDS iff r = s = 0.…”

Section: Solution Of the Master Equationmentioning

confidence: 99%

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Ghasemian

2023

Quantum Mach. Intell.

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Entangled state preparation and preservation are the cornerstones of any quantum information platform. However, the strongest adversaries in quantum information science are unwanted environmental effects such as decoherence and dissipation. Here, we address how to control and harness the dissipation that arises from the coupling of a system with its environment, to provide stationary entangled states for quantum machine learning. To do so, we design a dissipative quantum channel, i.e., a two-qubit system interacting with a squeezed vacuum field reservoir, and study the output state of the channel by solving the corresponding master equation, especially, in the small squeezing regime. We show that the time-dependent output state of the channel is the so-called two-qubit X-states that generalize many families of entangled two-qubit states. Also, by considering a general Bell diagonal state as the initial state of the system we reveal that this dissipative channel generates two well-known classes of entangled mixed state and Werner-like states in the steady-state regime. Moreover, this channel provides an efficient way to determine whether a given initial state results in a stationary entangled state or not. Finally, we examine the potential application of the designed two-qubit channel for quantum machine learning. Integrating the non-unitary transformation of the two-qubit channel and parallel-processed neural computing establishes the requirements for a meaningful quantum neural network.

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Section: Solution Of the Master Equationmentioning

confidence: 99%

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Ghasemian

2023

Quantum Mach. Intell.

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“…It has shown that quantum computers can solve a range of algorithms and complex protocols that conventional computers cannot. [ 31 ] Non‐local features, such as non‐classical correlation, non‐locality, and entanglement, are required by such quantum computers and related technology, [ 32,33 ] therefore, will remain the primary focus of this study.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Two‐Qubit Non‐Classical Correlations and Non‐Locality in Mixed Local Dephasing Noisy Channels

et al. 2022

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The dephasing effects of two independent local mixed static‐Ornstein Uhlenbeck (STC‐OUK) noisy channels on the dynamics of two‐qubit non‐classical correlations, non‐locality, and entanglement are addressed. Here, i) local quantum Fisher information; ii) local quantum uncertainty; iii) uncertainty‐induced non‐locality; iv) Bell non‐locality; and v) negativity to quantify two‐qubit non‐classical correlations, non‐locality and entanglement, respectively, and their loss under the influence of mixed noise are used. The findings show that measure (i) compared to measure (ii) remains more effective in demonstrating non‐classical correlations. For the two‐qubit state with maximum purity, measure (iii) remains less fragile to the mixed STC‐OUK noise than measure (iv) but gets more vulnerable as the initial purity of the two‐qubit state falls. It is intriguing that measures (i), (ii), and (v) completely freeze after a particular interval, yet measures (iii) and (iv) remains partially preserved indefinitely. When compared to other two‐qubit correlation quantifiers, measure (v) exhibits non‐Markovian behavior and the phenomenon of sudden death and birth. Markovian and non‐Markovian dynamical maps, and extended two‐qubit correlations, can be induced by optimizing the current configuration. Finally, under the influence of mixed dephasing effects, robust and strengthened quantum correlations beyond entanglement in the two‐qubit Werner state is shown.

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“…The accompanying open source Qiskit software [4] allows to compare simulation of any algorithm run on this software and the actual IBM quantum device, hence assessing the level of noise and gate imperfections and their effect on the output of any algorithm. Quite recently this has led many groups to run interesting algorithms on this quantum computer with promising results [5][6][7][8][9][10][11][12][13][14]. Among these works, the ones which have inspired our work are the study of a class of two-qubit states, namely Bell diagonal and Werner states, specially with regard to their correlation properties [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…Quite recently this has led many groups to run interesting algorithms on this quantum computer with promising results [5][6][7][8][9][10][11][12][13][14]. Among these works, the ones which have inspired our work are the study of a class of two-qubit states, namely Bell diagonal and Werner states, specially with regard to their correlation properties [9,10]. These are classical mixtures of the form,…”

Section: Introductionmentioning

confidence: 99%

“…These states are characterized by three independent real parameters, namely the three independent parameters which characterize the probability distribution {p i }. In [10], a complete study of correlation properties, i.e. entanglement [15][16][17], discord [18][19][20], non-locality [21,22], and steering [23,24] of these states were performed by first generating them on a circuit and then making appropriate measurements.…”

Section: Introductionmentioning

confidence: 99%

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Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

Karimi¹,

Shahbeigi²,

Karimipour³

2022

Phys. Scr.

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Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this Hamiltonian, we show that by only two qubits, one can simulate the dynamics of this system on the IBM quantum computer.

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Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer

Cited by 15 publications

References 55 publications

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Stationary states of a dissipative two-qubit quantum channel and their applications for quantum machine learning

Characterizing Two‐Qubit Non‐Classical Correlations and Non‐Locality in Mixed Local Dephasing Noisy Channels

Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer

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