Abstract We present a comprehensive approach to transform a partially entangled pure state into a maximally entangled state, utilizing only local operations and a single copy of the entangled state. Our approach eliminates the need for multiple copies of entangled states, bilateral operations, and the time-consuming partial-collapse weak measurements. Integrating ancilla qubits, rotation gates, and CNOT gates, we simplify the process of enhancing entanglement, achieving significant efficiency using only a single partially entangled state. Assuming perfect local operations, we showcase the efficacy of our method through both mathematical analysis and the practical implementation of the corresponding circuit in Qiskit. Furthermore, we explore the impact of imperfect local operations, specifically focusing on the CNOT gate and measurement, for a comprehensive analysis. Additionally, we address the case of unknown parameters in the partially entangled pure state and introduce a robust method to effectively handle this uncertainty, ensuring reliable entanglement fidelity optimization in practical situations. We extend our investigation to the application of our method to mixed initial entangled states. Our results demonstrate the reliability of our method in increasing entanglement even in the presence of phase damping and amplitude damping. Additionally, we illustrate its effectiveness in transforming specific mixed initial states in the presence of depolarization into states with enhanced entanglement.
Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.
We propose a measurement-based method to produce a maximally-entangled state from a partially-entangled pure state. Our goal can be thought of as entanglement distillation from a single copy of a partially-entangled state. The present approach involves local two-outcome weak measurements. We show that application of these local weak measurements leads to a probabilistic amplification of entanglement. In addition, we examine how the probability to find the maximally-entangled state is related to the entanglement of the input state. We also study the application of our method to a mixed initial state. We show that the protocol is successful if the separable part of the mixed initial state fulfils certain conditions.
Coherence-to-entanglement conversion transforms single-qubit superposition into a practical two-qubit resource, but noise limits this process in near-term quantum hardware. We derive closed-form benchmarks for a minimal CNOT primitive in which a coherent qubit and an incoherent ancilla generate entanglement before undergoing phase damping, global depolarizing, amplitude damping, or independent local depolarizing noise. Using the
ℓ1-norm of coherence and negativity, we prove the noiseless law
N0=Cℓ1/2, valid for arbitrary mixed inputs, and obtain exact negativities, survival fractions, and entanglement-sudden-death thresholds. For all
X-state-preserving channels, a master relation shows that entanglement loss results from the competition between coherence suppression and partial-transpose spectral shifts. Phase damping yields
η=1−p without finite-noise sudden death; global depolarization gives coherence-dependent sudden death; amplitude damping adds an excited-population penalty and sudden death only for
θ>π/4; while local depolarization is most destructive at equal depolarizing strength. The initial survival slopes,
−1,
−3/2,
−2, and
−3, act as compact noise fingerprints. Since concurrence satisfies
C=2N for the generated states, all robustness rankings remain unchanged. Mapping channel parameters to
T1,
Tφ, and average gate fidelity connects the theory to hardware-level performance.
We propose a scheme to enhance entanglement from amplitude damping or correlated amplitude damping decoherence. We show that entanglement sudden death time can be prolonged by the initial single-qubit operation combined with local filtering operation. For the amplitude damping channel case, we give the optimal single-qubit operation for arbitrary pure state [Formula: see text]. For the correlated amplitude damping channel case, we find that single-qubit operation on the initial state can not only enhance the final entanglement but also avoid entanglement sudden death. Compared to the previous schemes, the optimal operations and local filtering operations used in our scheme are independent with the decay parameters of the environment.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
Abstract In this article, we revisit the question of analysing the efficiencies of partially entangled states in three-qubit classes under real conditions. Our results show some interesting observations regarding the efficiencies and correlations of partially entangled states. Surprisingly, we find that the efficiencies of many three-qubit partially entangled states exceed that of maximally entangled three-qubit states under real noisy conditions and applications of weak measurements. Our analysis, therefore, suggests that the efficiencies of partially entangled states are much more robust to noise than those of maximally entangled states at least for the GHZ (Greenberger–Horne–Zeilinger) class states, for certain protocols; i.e. less correlations in the initially prepared state may also lead to better efficiency and hence one need not always consider starting with a maximally entangled state with maximum correlations between the qubits. For a set of partially entangled states, we find that the efficiency is optimal, independent of the decoherence and state parameters, if the value of weak measurement parameter is very large. For other values of the weak measurement parameter, the robustness of the states depends on the decoherence and state parameters. Moreover, we further show that one can achieve higher efficiencies in a protocol by using non-optimal weak measurement strengths instead of optimal weak measurement strengths.