Degree of coherence

Nilakantha Meher, Abu Musa Patoary, Girish Ashok Kulkarni +1 more

Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [ J. Opt. Soc. Am. B 36 , 2765 ( 2019 ) JOBPDE 0740-3224 10.1364/JOSAB.36.002765 ]. In this article, we use the same mathematical construction to define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, we first show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with the state and that a two-qubit state with an intrinsic degree of coherence less than 1 / 3 cannot violate Bell inequalities. We then show that the quantum discord of a two-qubit state, which quantifies the amount of quantum correlations available in the two-qubit state for certain tasks, is bounded from above by the intrinsic degree of coherence of the state. Next, in the context of two-particle entanglement, we show that the range of values that the concurrence of a two-qubit state can take is decided by the intrinsic degree of coherence of the two-qubit state together with that of the individual qubits. Finally, for the polarization two-qubit states generated by the parametric down-conversion of a pump photon, we propose an experimental scheme to measure the intrinsic degree of coherence of two-qubit states. We also present our theoretical study that shows how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.

Werner H. Lauterborn, Thomas Kurz

Ya-Ting Shao, Kai Yan, Yin‐Zhong Wu +1 more

The time evolution of multipartite quantum coherence is studied in a three-body spin system with an asymmetric interaction. The l1 norm measurement is used to estimate the degree of quantum coherence in the spin system. The decoherence of all components of quantum coherence in the three-body spin system is analyzed by the exact diagnolization and numerical method based on quantum master equation. The environmental noise induced by the spontaneous decay can be simulated by the quantum amplitude damping model. It is found that the time evolution of quantum coherence component is closely related to the quantum property of the whole initial state. When the initial state is a separable pure one, the asymmetric interactions can conduce to the enhancement of the degree of multipartite quantum coherence in a short time interval. Under the influence of quantum noise, the degree of quantum coherence decreases gradually. We pay much attention to the spatial distribution of the degree of quantum coherence in a many-body system. The additivity relationship of bipartite component and tripartite coherence can exist if the initial state is chosen to be a Werner-like state. This kind of the coherence additivity between all bipartite components and global coherence can be extended to an arbitrary N-body Werner-like state. But this additivity relationship depends on the l1 norm coherence measurement. Owing to the asymmetric interaction and noise, the degree of tripartite quantum coherence is more than the sum of all degrees of bipartite quantum coherence. The difference between the degree of tripartite coherence and the sum of all degrees of bipartite coherence is increased in a short time interval. The environmental noise can also suppress the difference in the coherence degree. The degree of the nearest neighboring bipartite coherence decreases more quickly than those of other bipartite coherences. The asymmetric interaction gives rise to the improvement in the degree of bipartite coherence and tripartite coherence. The coherence of the next-nearest neighboring two systems can be robust against the environmental noise. These results are helpful in preparing the multipartite quantum resources. We can utilize the system of coupled micro-cavities to realize the quantum spin system with controllable asymmetric interaction. In this way, the global coherence and bipartite coherence can be manipulated effectively by the quantum electromagnetic technology.

Mitchell Harling, Varun A. Kelkar, Chukwuemeka Okoro +3 more

The entropy associated with an optical field quantifies the field fluctuations and thus its coherence. Any binary optical degree-of-freedom (DoF) - such as polarization or the field at a pair of points in space - can each carry up to one bit of entropy. We demonstrate here that entropy can be reversibly swapped between different DoFs, such that coherence is converted back and forth between them without loss of energy. Specifically, starting with a spatially coherent but unpolarized field carrying one bit of entropy, we unitarily convert the coherence from the spatial DoF to polarization to produce a spatially incoherent but polarized field by swapping the entropy between the two DoFs. Next, we implement the inverse unitary operator, thus converting the coherence back to yield once again a spatially coherent yet unpolarized field. We exploit the intermediate stage between the two coherence conversions - where the spatial coherence has been converted to the polarization DoF - to verify that the field has become immune to the deleterious impact of spatial phase scrambling. Maximizing the spatial entropy protects the spatial DoF by preventing it from taking on any additional fluctuations. After the second coherence conversion, spatial coherence is readily retrieved, and the effect of spatial phase scrambling circumvented.

Werner H. Lauterborn, Thomas Kurz, Martin Wiesenfeldt