Enhancing entanglement and total correlation dynamics via local unitaries

The interaction with the environment is one of the main obstacles to be circumvented in practical implementations of quantum information tasks. The use of local unitaries, while not changing the initial entanglement present in a given state, can enormously change its dynamics through a noisy channel, and consequently its ability to be used as a resource. In this way, local unitaries provide an easy and accessible way to enhance quantum correlations in a variety of different experimental platforms. Given an initial entangled state and a certain noisy channel, what are the local unitaries providing the most robust dynamics? In this paper we solve this question considering two-qubit states, together with paradigmatic and relevant noisy channels, showing its consequences for teleportation protocols and identifying cases where the most robust states are not necessarily the ones imprinting the least information about themselves into the environment. We also derive a general multipartite law relating the interplay between the total correlations in the system and environment with their mutual information built up over the noisy dynamics. Finally, we employ the IBM Quantum Experience to provide a proof-of-principle experimental implementation of our results.

Figure 1

Circuits implementing the amplitude damping channel. (a) For the state $|{\mathrm{\Phi }}_0\rangle =(1/\sqrt{2})\left(\right|00\rangle +|11\rangle )$. (b) For the state $|{\mathrm{\Phi }}_{\pi /2}\rangle =(1/\sqrt{2})\left(\right|01\rangle +|10\rangle )$. All the qubits in the circuit are initialized as $|0\rangle$. Notice that the single difference between both circuits is an $X$ gate applied in the beginning of the circuit. As we will explore in detail, this is already enough to enhance substantially the dynamics of the correlations in the system of interest.

Figure 2

Dynamics of correlations for the amplitude damping dynamics. (a) Increase in the total correlations of the environment. (b) Decrease of total correlation of the system. (c) Mutual information built between system and environment. The system is initially in $|01\rangle +|10\rangle$ [yellow curve—up in (a) and (b), down in (c)—for theoretical result and yellow dots for experimental results] or $|00\rangle +|11\rangle$ [blue—down in (a) and (b), up in (c)—curve for theoretical result and blue dots for experimental results]. All experimental results were obtained using the quantum computer ibmq_manila from IBM Q-Experience [32, 34].

Figure 3

Dynamics of correlations for the dephasing dynamics. (a) Increase in the total correlations of the environment. (b) Decrease of the total correlation of the system. (c) Mutual information built between system and environment. We consider that the system is initially in the quantum state $|01\rangle +|10\rangle$ [yellow curve—down in (a) and (b), up in (c)] or in the state $|0+\rangle +|1-\rangle$ (blue curve—up in (a) and (b), down in (c)].

Figure 4

The dynamics of $\mathcal{N}$ (continuous curves for theoretical results and dots for experimental ones), $\mathcal{C}$ (inset), $E_E\left({\varrho }_{SE}\right)$ (dashed curves for theoretical results and dots for experimental ones) for the maximally entangled state $|{\mathrm{\Phi }}_{\gamma =0}\rangle$ (blue—up in the main graph, down in the inset) and $|{\mathrm{\Phi }}_{\gamma =\pi /2}\rangle$ (red—down in the main graph, up in the inset) undergoing the AD channel. Note that the ordering given by $\mathcal{N}$ and $\mathcal{C}$ is reversed. Surprisingly the most robust state according to the negativity is exactly the one generating more entanglement with the environment. All experimental results were obtained using the quantum computer ibmq_manila from IBM Q-Experience [34].

Figure 5

Negativity dynamics for the AD channel. The blue curve, starting with $\mathcal{N}=1.0$, and dots represent the maximally entangled state, and the red curve and dots the nonmaximally entangled state (we use $\theta =\frac{0.7\pi }{4}$ in this example), curve for theoretical results and dots for experimental results.