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IEEE Journal of Selected Topics in Quantum Electronics

$N$-Qubit State Protection Against Amplitude Damping by Quantum Feed-Forward Control and its Reversal

Sajede Harraz, Shuang Cong

Published Feb 2, 2020• 13 citations
Publisher

Abstract

We propose a state protection scheme of quantum feed-forward control and its reversal (QFFCR) by quantum weak measurement and quantum control to protect the arbitrary N-qubit state in amplitude-damping channel (ADC). Before the state enters the ADC, a weak measurement and an offsetting operation are made to make the state almost immune to the effect of ADC. After the state passes the ADC, the reversed offsetting operation and a correction rotation are applied to recover the state. Unlike most previous state protection schemes, ours does not use weak measurement reversal, but a correction rotation to bring back the state to its initial amount. Our protection scheme can also protect entangled states even for heavy damping probabilities effectively. Fidelity and success probability are used to evaluate the effect of the proposed scheme. The general formula for complete recovery and the total success probability of N-qubit system are derived. The effectiveness of our control scheme is demonstrated by simulation results.

DOI
10.1109/jstqe.2020.2969574

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NNN-Qubit State Protection Against Amplitude Damping by Quantum Feed-Forward Control and its Reversal
We propose a state protection scheme of quantum feed-forward control and its reversal (QFFCR) by quantum weak measurement and quantum control to protect the arbitrary N-qubit state in amplitude-damping channel (ADC). Before the state enters the ADC, a weak measurement and an offsetting operation are made to make the state almost immune to the effect of ADC. After the state passes the ADC, the reversed offsetting operation and a correction rotation are applied to recover the state. Unlike most previous state protection schemes, ours does not use weak measurement reversal, but a correction rotation to bring back the state to its initial amount. Our protection scheme can also protect entangled states even for heavy damping probabilities effectively. Fidelity and success probability are used to evaluate the effect of the proposed scheme. The general formula for complete recovery and the total success probability of N-qubit system are derived. The effectiveness of our control scheme is demonstrated by simulation results.
We propose a scheme of feed-forward control and its reversal for protecting quantum state against decoherence. Before the noise channel our pre-weak measurement and feed-forward are simply to change the protected state into the state almost immune to the noise channel, and after the channel our reversed operations and post-weak measurements are simply to restore the protected state. Unlike most previous state protection schemes, ours only concerns the noise channel and does not care about the protected state. We show that our scheme can effectively protect unknown states, nonorthogonal states, and entangled states against amplitude damping noise. Our scheme has the merit of protecting quantum states against heavy amplitude damping noise, and can perfectly protect some specific nonorthogonal states in an almost deterministic way, which might find some applications in current quantum communication technology. And it is most important that our scheme is experimentally available with current technology.
In this paper we propose a scheme by using weak-measurement-based pre- and post-flips (WMPPF) to protect the average quantum Fisher information (QFI) in the independent amplitude-damping channel (ADC) for N-qubit GHZ state and generalized N-qubit GHZ states. We also discuss the weak measurement and quantum measurement reversal (WMQMR) with the same ADC. Based on the analytical and numerical results we obtain the main result: the WMPPF can reduce the effect of dissipation on the average QFI of the phase or the frequency for GHZ state and some generalized GHZ states, and the WMQMR can reduce the effect of dissipation on the average fidelity for GHZ state and generalized GHZ states in ADC. Comparing QFI with fidelity for WMPPF or for WMQMR, a scheme protecting the average fidelity does not necessarily protect the average QFI, even with the same parameters, and vice versa. We also focus on the average QFI versus N in the phase estimation and the frequency estimation of WMPPF, both of which show the advantages over the do-nothing (DN) case. From the investigation of the QFI of weight factor, we find that increasing qubit number can protect it both for WMPPF and for DN.
Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.
In this paper we study the protection of N-qubit Greenberger-Horne- Zeilinger (GHZ) state and generalized N-qubit GHZ states in amplitude damping channel by means of quantum weak measurement and flip operations. We derive the explicit formulas of the performances of the protection scheme: average fidelity, average probability and the average quantum fisher information (QFI). Moreover, the analytical results for maximizing the average fidelity and probability are obtained. We show that our scheme can effectively protect the average QFI of phase for GHZ states and generalized GHZ states. The proposed scheme has the merit of protecting GHZ state and the QFI of phase against heavy amplitude damping noise. Further we show that for some generalize GHZ state, the proposed scheme can protect the state with probability one and fidelity more than 99%.
We investigate the entanglement protection of a hybrid qubit–qutrit system under amplitude damping decoherence by employing weak measurement and reversal. We examine two typical families of initially entangled qubit–qutrit states (i.e. one-parameter and two-parameter qubit–qutrit states). We find that the qubit–qutrit entanglement decays monotonically as the decoherence strength increases, and may go through a sudden death for some initial states. However, we can completely defeat amplitude damping decoherence and recover the initial entanglement perfectly for any initial states by means of the combination of prior weak measurement and subsequent optimal weak measurement reversal. The only price that we have to pay is the very low success probability.
High-dimensional quantum communication plays an important role in long-distance quantum communication. It is shown that two-qubit quantum entanglement can be protected from amplitude damping decoherence. We study the effect of amplitude damping decoherence on two-qubit high-dimensional quantum entanglement. The negativity for high-dimensional quantum entanglement with or without quantum weak measurement and the reversal in amplitude damping decoherence are presented. We found that nonmaximally entangled state may have better performance than maximally entangled state in amplitude damping decoherence. Moreover, we show that arbitrary high-dimensional quantum entanglement can be protected from amplitude damping decoherence by weak measurement and the reversal. The results of our protocol are in agreement with previous analysis for the case of qubits and qutrits.