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arXiv:2411.03627 · Physical Review A

Nonlocal advantages of quantum imaginarity

Zhi-Wei Wei, Shao-Ming Fei

Published Nov 5, 2024• 25 citations
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Abstract

Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity ${l}_{1}$-norm and relative entropy, we derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not vice versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states.

DOI
10.1103/physreva.110.052202

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Quantum imaginarity and quantum nonlocality capture the essence of quantumness of a physical system from different aspects. We establish a connection between the imaginarity and quantum nonlocality in any two-qubit states. Based on the imaginarity l1{l}_{1}l1​-norm and relative entropy, we derive complementary relations among the quantum imaginarities with respect to any set of mutually unbiased bases for arbitrary qubit states. Based on these complementary relations, we introduce the nonlocal advantage of quantum imaginarity (NAQI). We show that any two-qubit state with NAQI is quantum steerable, but not vice versa. In addition, we investigate the exclusion property of NAQI in three-qubit pure states.
Quantum imaginarity is a distinct resource in quantum information theory, yet its nonlocal properties have not been fully explored. Here, we report an experimental study of the nonlocal advantage of quantum imaginarity (NAQI), in which local measurements on one subsystem can steer the average imaginarity of the conditional states of the other subsystem beyond the corresponding classical bound. The l1l_1l1​-norm of imaginarity inequality is adopted as an experimentally accessible witness. A hybrid optimization algorithm that combines a genetic algorithm with sequential quadratic programming is developed to avoid local optima and accelerate the search for optimal measurement settings. Using polarization-encoded photonic qubits, we prepare two classes of two-qubit Bell-diagonal states and experimentally characterize the imaginarity of the conditional states following local measurements. Clear violations of the l1l_1l1​-norm of imaginarity inequality are observed, providing an experimental certification of NAQI. We further investigate the relationship among NAQI, the nonlocal advantage of quantum coherence (NAQC), and Bell nonlocality based on their respective inequality criteria. For the two-qubit Werner states considered in this work, the regions of states that violate the respective criteria satisfy DNAQC⊂DNAQI⊂DBN\mathcal{D}_{\rm NAQC}\subset\mathcal{D}_{\rm NAQI}\subset\mathcal{D}_{\rm BN}DNAQC​⊂DNAQI​⊂DBN​. Our work provides an experimental realization of NAQI and a comparison of different forms of quantum nonclassicality in a photonic platform.
A bipartite state is said to be steerable if and only if it does not have a single-system description, i.e., the bipartite state cannot be explained by a local hidden state model. Several steering inequalities have been derived using different local uncertainty relations to verify the ability to control the state of one subsystem by the other party. Here, we derive complementarity relations between coherences measured on mutually unbiased bases using various coherence measures such as the l1{l}_{1}l1​-norm, relative entropy, and skew information. Using these relations, we derive conditions under which a nonlocal advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such an advantage.
Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of the Hawking effect on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, it is significantly affected by Hawking radiation, exhibiting a pronounced difference between physically accessible and inaccessible regions. It is suppressed in the physically accessible region with increasing Hawking temperature and may vanish, while remaining absent in the physically inaccessible region across the parameter regime. For assisted imaginarity distillation, the Hawking effect modifies the assisted fidelity in a state-dependent manner. In the physically accessible region, the fidelity generally decreases with increasing temperature, indicating reduced distillation capability, whereas the physically inaccessible region exhibits the opposite monotonic trend, indicating enhanced distillation capability. These results highlight distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in curved spacetime.
Nonlocal advantage of quantum coherence (NAQC) based on coherence complementarity relations is generally viewed as a stronger nonclassical correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must be an entangled state, which demonstrates that the criterion of NAQC can also be regarded as an entanglement witness. In this paper, we experimentally investigate the NAQC for Bell-diagonal states with high fidelity in an optics-based platform. We perform local measurements on a subsystem in three mutually unbiased bases and reconstruct the density matrices of the measured states by a quantum state tomography process. By analyzing characteristics of the l1{l}_{1}l1​ norm, relative entropy, and skew information of coherence with parameters of quantum states, NAQC for the quantum states is accurately captured, and it shows that our experimental results are well compatible with the theoretical predictions. Our results have shown that NAQC could be a new kind of entanglement witness and a useful physical resource for quantum information processing.
Coherences in mutually unbiased bases of states of an isolated quantum system follow a complementarity relation. The nonlocal advantage of quantum coherence (NAQC), defined in a bipartite scenario, is a situation in which the average quantum coherences of the ensembles of one subsystem, effected by a measurement performed on the other subsystem, violate the complementarity relation. We analyze two criteria to detect NAQC for bipartite quantum states. We construct a more generalized version of the criterion to detect NAQC that is better than the standard criterion as it can capture more states exhibiting NAQC. We prove the local unitary invariance of these NAQC criteria. Further on, we focus on investigating the monogamy properties of NAQC in the tripartite scenario. We check for monogamy of NAQC from two perspectives, differentiated by whether or not the nodal observer in the monogamy relation performs the measurement for the nonlocal advantage. We find in particular that in the case where the nodal observer does not perform the measurement, a strong monogamy relation---an exclusion principle---is exhibited by NAQC.
Complex numbers are central to the formulation of quantum mechanics, yet their role as a genuine resource is only beginning to be understood. In this work, we demonstrate that quantum states with intrinsically complex amplitudes provide a fundamental advantage in state discrimination. We construct a set of five orthogonal three qubit pure states and show that the set is strongly nonlocal if and only if it includes imaginary components. Such a set becomes locally indistinguishable not only under local measurements but also against bipartite joint measurements. This enhanced robustness makes imaginarity a valuable resource for quantum cryptography since information encoded in these states remains secure against collaborative group attacks. Our results highlight a new operational role of complex numbers in quantum theory and establish imaginarity as a key enabler of cryptographic security. However, we reconstruct the set by replacing the only product state with a biseparable state whose shared entanglement between two parties nullifies the effect of imaginarity in exhibiting strong nonlocality. In fact, we show how entangling correlations between two distant parties can dilute the effect of imaginarity, and conversely, how imaginarity itself can mimic the role of entanglement. Nevertheless, the set spans a locally indistinguishable subspace, while its complement, in turn, produces distillable genuine entanglement. Notably, this is the smallest possible Unextendible Biseparable Basis (UBB) that resolves the open problem regarding the existence of a UBB of cardinality d2+d−1d^2+d-1d2+d−1 in d⊗3d^{\otimes 3}d⊗3. Our construction yields a highly powerful set, rich in resources from multiple perspectives of quantum information theory, including many-copy discrimination, unambiguous identification, entanglement creation from product state, and non-entangling perturbations.