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arXiv:1708.08208 · Physical Review A

Ultimate entanglement robustness of two-qubit states against general local noises

Sergey N. Filippov, Vladimir V. Frizen, Daria V. Kolobova

Published Jan 19, 2018• 16 citations
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Abstract

We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises, such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two times longer than conventional maximally entangled states.

DOI
10.1103/physreva.97.012322

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We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises, such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two times longer than conventional maximally entangled states.
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Abstract We studied the entangling power of two pure global noises, i.e. amplitude damping noise and classic noise. The entangling power of the two-qubit amplitude damping global noise periodically oscillates with time. Additionally, the entangling power of two-qubit global classical noise increases exponentially with time. The maximum entangling power of both of them exceeds that of the perfect entanglers. Based on this, we propose the conditions for generating a maximally entangled state with global noise acting on a two-qubit separable state. Only if the two-qubit composite system, which is initially in one of those product states: 1 2 ( | 0 ⟩ ± | 1 ⟩ ) ⊗ 1 2 ( | 0 ⟩ ± | 1 ⟩ ) , | 10 ⟩ and | 01 ⟩ suffers an amplitude damping global noise, can we prepare this system in the maximally entangled state by appropriately controlling the evolution time of amplitude damping. Finally, we investigate the disentanglement of the maximum entangled Bell state using these two types of global noise. The two global noises cannot completely disentangle the Bell states Φ ± . Under the influence of amplitude damping global noise, the entanglement of Bell state Ψ + undergoes a cyclical variation, alternating between disappearance and recovery to reach maximum entanglement within one period. The entanglement of either Bell state Ψ + or Ψ − is completely independent of global classical noise. The entanglement of Bell state Ψ − is also robust against amplitude damping global noise.
Maximally entangled states---a resource for quantum information processing---can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no local postprocessing. In particular, the optimal singlet fraction is achieved by transmitting part of an appropriate pure entangled state, which is maximally entangled if and only if the channel is unital. A linear function of the optimal singlet fraction is also shown to be an upper bound on the distillable entanglement of the mixed state dual to the channel.
Can entangled noise erase entanglement more efficiently than separable noise? Standard robustness restricts the added noise to separable states; generalized robustness allows any state. We prove that the two costs coincide for every two-qubit state and give an explicit full-rank qubit--qutrit state with a strict gap. Positivity under partial transpose (PPT) characterizes separability in both dimensions, so the boundary is not caused by a failure of the PPT criterion. Instead, product-vector geometry permits a rank-one bridge between the two-qubit dual optimizations and supplies a two-dimensional completely entangled subspace for the qubit--qutrit separation. Local isometric embeddings complete the finite-dimensional bipartite classification, also for any fixed multipartite cut. Combined with known three-qubit separation, the result classifies universal equality relative to full separability in all finite multipartite systems.
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory. In this work, we explore the behavior of the quantum-memory-assisted entropic uncertainty relation under the influence of local unital and nonunital noisy channels. For a class of Bell-diagonal states, we demonstrate that while the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may reduce the amount of uncertainty in the long-time limit. The mechanism behind this phenomenon is also explored by using two dissimilar methods.
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localization, and that the optimal strategy for reducing a three-qubit GHZ state to a two-qubit one via local measurements and classical communications in the amplitude-damping case is different from that in the noise-free case. We also show that the idea of entanglement localization could be utilized to improve the quality of bipartite entanglement distributing through amplitude-damping channels. These findings might shed a new light on entanglement manipulations and transformations.