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Physical Review A

Experimental investigation of quantum discord in spin-orbit X states

V. S. Lamego, D. G. Braga, W. F. Balthazar, J. A. O. Huguenin

Published Sep 3, 2024• 6 citations
Publisher

Abstract

We perform an experimental study of quantum discord on spin-orbit modes of an intense laser beam, analogous to different X states. These modes are prepared through the incoherent superposition of different intense laser beams, encoding a two-qubit system in both polarization and the first-order Hermite-Gaussian modes [as proposed in Phys. Rev. A 103, 022411 (2021)]. We characterize these modes by using all-optical tomography and calculated entropic quantum discord. Remarkably, even for high-fidelity mode reconstruction, the computation of quantum discord showed significant deviations from theoretical expectations. Then, we proposed a simple model based on noisy measurements that showed a small degradation of the fidelity of the output modes, giving rise to the strong deviation of the discord. Our results, both experimental data and the theoretical predictions, demonstrate good agreement.

DOI
10.1103/physreva.110.032601

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We perform an experimental study of quantum discord on spin-orbit modes of an intense laser beam, analogous to different X states. These modes are prepared through the incoherent superposition of different intense laser beams, encoding a two-qubit system in both polarization and the first-order Hermite-Gaussian modes [as proposed in Phys. Rev. A 103, 022411 (2021)]. We characterize these modes by using all-optical tomography and calculated entropic quantum discord. Remarkably, even for high-fidelity mode reconstruction, the computation of quantum discord showed significant deviations from theoretical expectations. Then, we proposed a simple model based on noisy measurements that showed a small degradation of the fidelity of the output modes, giving rise to the strong deviation of the discord. Our results, both experimental data and the theoretical predictions, demonstrate good agreement.
We perform an experimental investigation of Quantum Discord with Spin-Orbit X-states. These states are prepared through the incoherent superposition of different laser beans, where a two-level system is encoded in polarization and the first-order Hermitian-Gaussian modes, as proposed in Phys. Rev. A 103,0022411 (2022). We characterize different classes of spin-orbit X-states by performing an all-optical tomography for polarization and first-order transverse mode degrees of freedom. We also perform a study on the dependence of Discord with respect to the Fidelity of spin-orbit modes, revealing that Discord is very sensitive to incoherent noise. Our experimental results align with the theoretical predictions of Quantum Discord when accounting for the effect of fidelity. These results reinforce the spin-orbit modes as an important platform for quantum information processing. On the other hand, the need of astigmatic optical elements to implement unitary operations required by quantum information protocols implies in a loss of fidelity and quantum correlations. Alternative methods to manipulate spin-orbit modes are welcome.
We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond tomography may be effectively implemented. Our results, together with the lack of an analytic formula for the entropic discord of a generic two-qubit state, demonstrate that the estimation of quantum discord is an intrinsically noisy procedure. Besides, we question the use of fidelity as a figure of merit to assess quantum correlations.
We investigate evolution of quantum correlations in ensembles of two-qubit nuclear spin systems via nuclear magnetic resonance techniques. We use discord as a measure of quantum correlations and the Werner state as an explicit example. We, first, introduce different ways of measuring discord and geometric discord in two-qubit systems and then describe the following experimental studies: (a) We quantitatively measure discord for Werner-like states prepared using an entangling pulse sequence. An initial thermal state with zero discord is gradually and periodically transformed into a mixed state with maximum discord. The experimental and simulated behavior of rise and fall of discord agree fairly well. (b) We examine the efficiency of dynamical decoupling sequences in preserving quantum correlations. In our experimental setup, the dynamical decoupling sequences preserved the traceless parts of the density matrices at high fidelity. But they could not maintain the purity of the quantum states and so were unable to keep the discord from decaying. (c) We observe the evolution of discord for a singlet-triplet mixed state during a radio-frequency spin-lock. A simple relaxation model describes the evolution of discord, and the accompanying evolution of fidelity of the long-lived singlet state, reasonably well.
Gaussian quantum discord is a measure of quantum correlations in gaussian systems. Using gaussian discord, we quantify the quantum correlations of a bipartite entangled state and a separable two-mode mixture of coherent states. We experimentally analyze the effect of noise addition and dissipation on gaussian discord and show that the former noise degrades the discord, while the latter noise for some states leads to an increase of the discord. In particular, we experimentally demonstrate the near death of discord by noisy evolution and its revival through dissipation.
Abstract Structured light plays an essential role in several quantum information protocols by using the degrees of freedom of light to encode qubits. For exploring different correlations, especially in mixed states, such as discord, it is necessary to prepare partially entangled states. In this work, we present a theoretical and experimental study of a partial nonseparable spin-orbit modes. By exploring classical-quantum analogy, we perform the measurement of the concurrence of partially separable modes directly from projective measurement of polarization. The results show a clear agreement with predictions of quantum theory for partially entangled states. We also perform a study of Clauser, Horn, Shimony, and Holt (CHSH) inequality and show that partial violation is observed in entire agreement with the expected by quantum theory. For the maximally nonseparable mode, we achieve a violation of S = 2.73 ± 0.03 , one of the higher ones observed for spin-orbit modes based on our best knowledge.
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical formulation. The tracing over the qubit in the entropic calculation is reduced to a very simple prescription. And, when the d-dimensional system is a so-called X state, the density matrix having non-zero elements only along the diagonal and anti-diagonal so as to appear visually like the letter X, the entropic calculation can be carried out analytically. Such states of the full bipartite qubit-qudit system may be named "extended X states", whose density matrix is built of four block matrices, each visually appearing as an X. The optimization involved in the entropic calculation is generally over two parameters, reducing to one for many cases, and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate. Our results also apply to states of a N-qubit system, where "extended X states" consist of (2^(N+2) - 1) states, larger in number than the (2^(N+1) - 1) of X states of N qubits. While these are still smaller than the total number (2^(2N) - 1) of states of N qubits, the number of parameters involved is nevertheless large. In the case of N = 2, they encompass the entire 15-dimensional parameter space, that is, the extended X states for N = 2 represent the full qubit-qubit system.