The ability of achieving strong quantum spatial correlations has helped the emergence of quantum information science. In contrast, how to achieve strong quantum temporal correlations (QTCs) has remained as a long-standing challenge, thus hindering their applications in time-domain quantum control. Here we experimentally demonstrate that by using a parity-time ( PT )–symmetric single ion, the conventional QTC limit known as the Lüders bound can be well surpassed within a standard measurement scenario, approaching the predicted maximum QTC value. Our work, as a step toward quantum engineering of PT devices in the time domain, can stimulate more efforts on operating various quantum devices with the aid of strong QTC resources.
The ability of achieving strong quantum spatial correlations has helped the emergence of quantum information science. In contrast, how to achieve strong quantum temporal correlations (QTCs) has remained as a long-standing challenge, thus hindering their applications in time-domain quantum control. Here we experimentally demonstrate that by using a parity-time ( PT )–symmetric single ion, the conventional QTC limit known as the Lüders bound can be well surpassed within a standard measurement scenario, approaching the predicted maximum QTC value. Our work, as a step toward quantum engineering of PT devices in the time domain, can stimulate more efforts on operating various quantum devices with the aid of strong QTC resources.
Abstract The powerful ability of achieving and manipulating strong spatial quantum correlations has helped the emergence of quantum information science. In contrast, strong temporal quantum correlations (TQC), playing an essential role in a wide range of physical and biological processes, have remained an elusive and long-standing challenge, hindering their practical applications. Here, for the first time, we experimentally demonstrate how to break the Lüders bound and to achieve the ultimate upper limit of TQC, by using a parity-time (PT)-symmetric single-ion system, within a standard measurement scenario. We achieve this goal by approaching an exceptional point (EP) in such a system, confirming the power of PT symmetry and non-Hermitian phase transition in enhancing purely quantum effects. Our work not only removes an important obstacle for TQC-based quantum engineering applications, but also sheds new light on operating quantum devices at EPs.
Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of novel phenomena and applications beyond the Hermitian framework have been uncovered. However, unique features of non-Hermitian quantum correlations, especially in the time domain, still remain to be explored. Here, for the first time, we experimentally achieve this goal by using a parity-time (PT)-symmetric trapped-ion system. The upper limit of temporal quantum correlations, known as the algebraic bound, which has so far not been achieved in the standard measurement scenario, is reached here by approaching the exceptional point (EP), thus showing the unexpected ability of EPs in tuning temporal quantum correlation effects. Our study, unveiling the fundamental interplay of non-Hermiticity, nonlinearity, and temporal quantum correlations, provides the first step towards exploring and utilizing various non-Hermitian temporal quantum effects by operating a wide range of EP devices, which are important for both fundamental studies and applications of quantum EP systems.
Macrorealistic description governing the classical realm is known to get uprooted in the quantum domain. The Leggett-Garg inequality [A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985)] proposes to probe the macrorealistic limit emerging from the quantum scenario. It places a bound on the linear combinations of temporal correlations of observables measured sequentially at different time intervals. Violation of the Leggett-Garg inequality, up to the so-called temporal Tsirelson bound (TTB), has been realized in the quantum domain. It is important to understand whether quantum theory permits larger violation beyond the TTB and up to the algebraic maximum value of the Leggett-Garg inequality. To this end, it has been shown [C. Budroni and C. Emary, Phys. Rev. Lett. 113, 050401 (2014)] that a three-term Leggett-Garg inequality can be violated beyond the TTB 3/2 in the time evolution of N>2 level quantum systems by choosing suitable measurement schemes and state-update rules. Furthermore, it is revealed that the algebraic maximum value 3 can be realized in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. Their measurement scheme rules out violation of the Leggett-Garg inequality beyond the TTB by a qubit. Being genuinely quantum in nature, we ask whether such enhanced violation of the Leggett-Garg inequality could be witnessed in a qubit itself. Here, we show that a qubit undergoing time evolution generated by a non-Hermitian PT-symmetric Hamiltonian indeed violates the three-term Leggett-Garg inequality beyond the TTB and up to its algebraic maximum value 3.
Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In two-level quantum systems - qubits - unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to 22 or 1.5 respectively. Experiments with state-of-the-art qubits have approached the spatial, Bell and temporal, Leggett-Garg quantum correlation bounds. Here, using a dissipative, trapped 40Ca+ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.703(4) for the Leggett-Garg parameter K3, clearly exceeding the hitherto inviolable Lüder's bound of 1.5. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics. Distinct evolution speeds for antipodal qubit states, which violate the unified (Mendelstam-Tamm or Margolus-Levitin) bound τQSL for the transit time based on quantum speed limit, result in the super-quantum K3 values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics.
The Leggett-Garg inequality (LGI) delineates a boundary between quantum and classical systems. While the temporal quantum correlations represented by LGIs have been extensively investigated in the Hermitian domain, the exploration of LGIs under non-Hermitian conditions remains scarce. Theoretical conjectures posit that nonunitary dynamics could transcend the boundary of LGIs set by Hermitian quantum mechanics, yet its empirical validation is lacking. Here, we demonstrate the enhanced violation of LGIs in a non-Hermitian system of a parity-time (PT)-symmetric trapped-ion qubit. The upper bounds of both the third-order parameter K3 and fourth-order parameter K4 increase with dissipation and can reach the maximum value when the system approaches the exceptional point, where ${K}_{3}={C}_{21}+{C}_{32}\ensuremath{-}{C}_{31}$ is comprising three two-time correlations and ${K}_{4}={C}_{21}+{C}_{32}+{C}_{43}\ensuremath{-}{C}_{41}$ is comprising four correlations. We also find that the lower bounds of K3 and K4 exhibit distinctive behaviors, where the lower bound of K3 remains constant, but that of K4 depends on the target states and measurement operators. These findings reveal a pronounced correlation between the dissipative nature of a quantum system and its temporal correlations.
Measurements on a single quantum system at different times reveal rich nonclassical correlations similar to those observed in spatially separated multipartite systems. Here we introduce a theory framework that unifies the description of temporal, spatial, and spatiotemporal resources for quantum correlations. We identify and experimentally demonstrate simple cases where an exact mapping between the domains is possible. We then identify correlation resources in arbitrary situations, where not all spatial quantum states correspond to a process and not all temporal measurements have a spatial analog. These results provide a starting point for the systematic exploration of multipoint temporal correlations as a powerful resource for quantum information processing.