Geometry of Einstein-Podolsky-Rosen Correlations

Compatibility of Generalized Noisy Qubit Measurements

It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine the critical visibility such that all qubit measurements, i.e., all positive operator-valued measures (POVMs), become compatible, i.e., jointly measurable. In addition, we apply our methods to quantum steering and Bell nonlocality. We obtain a tight local hidden state model for two-qubit Werner states of visibility 1/2. This determines the exact steering bound for two-qubit Werner states and also provides a local hidden variable model that improves on previously known models. Interestingly, this proves that POVMs are not more powerful than projective measurements to demonstrate quantum steering for these states.

Contextuality as a Precondition for Quantum Entanglement

Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality, can be observed if quantum states are prepared and then subjected to sequences of measurements. We use robust remote state preparation to connect the nonlocal and sequential scenarios and provide an intimate connection between different resources: We prove that entanglement in a nonlocal scenario can arise only if there is preparation and measurement contextuality in the corresponding sequential scenario and that the absence of entanglement implies the absence of contextuality. As a direct consequence, our result allows us to translate any inequality for testing preparation and measurement contextuality into an entanglement test; in addition, entanglement witnesses can be used to design novel contextuality inequalities.

Detecting the steerability through an optimized steering criterion in two-photon systems

The steerability of a quantum state can be detected by steering inequalities. The linear steering inequalities show that more steerable states can be discovered with the increase of measurements. In order to detect more steerable states in two-photon systems, we first theoretically derive an optimized steering criterion based on infinity measurements for an arbitrary two-qubit state. The steering criterion is only determined by the spin correlation matrix of the state, and do not require infinity measurements. Then, we prepared the Werner-like states in two-photon systems, and measure their spin correlation matrices. Finally, we apply three steering criteria, which include our steering criterion, the three-measurement steering criterion and the geometric Bell-like inequality, to distinguish the steerability of these states. The results show that our steering criterion can detect the most steerable states under the same experimental conditions. Thus, our work provides a valuable reference for detecting the steerability of quantum states.

Reliable experimental manipulation of quantum steering direction

Noise-adding methods have been widely used to manipulate the direction of quantum steering, but all related experimental schemes only worked under the assumption that Gaussian measurements were performed and ideal target states were accurately prepared. Here, we prove, and then experimentally observe, that a class of two-qubit states can be flexibly changed among two-way steerable, one-way steerable and no-way steerable, by adding either phase damping noise or depolarization noise. The steering direction is determined by measuring steering radius and critical radius, each of which represents a necessary and sufficient steering criterion valid for general projective measurements and actually prepared states. Our work provides a more efficient and rigorous way to manipulate the direction of quantum steering, and can also be employed to manipulate other types of quantum correlations.

Protecting nonlocal quantum correlations in correlated squeezed generalized amplitude damping channel

Nonlocal quantum correlations, such as quantum entanglement, quantum steering, and Bell nonlocality, are crucial resources for quantum information tasks. How to protect these quantum resources from decoherence is one of the most urgent problems to be solved. Here, we investigate the evolution of these correlations in the correlated squeezed generalized amplitude damping (SGAD) channel and propose a scheme to protect them with weak measurement (WM) and quantum measurement reversal (QMR). Compared with the results of the uncorrelated SGAD channel, we find that when $$n=1$$ n = 1 , correlation and squeezing effects can prolong the survival time of quantum entanglement, Bell nonlocality, and quantum steering by about 152 times, 207 times, and 10 times, respectively. In addition, local WM and QMR can effectively recover the disappeared nonlocal quantum correlations either in uncorrelated or completely correlated SGAD channels. Moreover, we find that these initial nonlocal quantum correlations could be drastically amplified under the correlated channel. And the steering direction can be flexibly manipulated either by changing the channel parameters or the strength of WM and QMR. These results not only make a step forward in suppressing decoherence and enhancing quantum correlation in noise channels, but also help to develop relevant practical applications.

Preparation of quantum correlations assisted by a steering Maxwell demon

A Maxwell demon can reduce the entropy of a quantum system by performing measurements on its environment. The nonsignaling theorem prevents the demon from affecting the average state of the system. We study the preparations of quantum correlations from a system qubit and an auxiliary qubit, assisted by a demon who obtains information of the system qubit from measurements on its environment. The demon can affect the postmeasured states of system by choosing different measurements, which establishes the relationships between quantum steering and other correlations in the thermodynamic framework. We present the optimal protocols for creating mutual information, entanglement, and Bell-nonlocality. These maximal correlations are found to relate exactly to the steerable boundary of the system-environment state with maximally mixed marginals. We also present upper bounds of the prepared correlations by utilizing classical environment-system correlation, which can be regarded as steering-type inequalities bounding the correlations created with the aid of classical demons.

Some Quantum Measurements with Three Outcomes Can Reveal Nonclassicality where All Two-Outcome Measurements Fail to Do So

Measurements serve as the intermediate communication layer between the quantum world and our classical perception. So, the question of which measurements efficiently extract information from quantum systems is of central interest. Using quantum steering as a nonclassical phenomenon, we show that there are instances where the results of all two-outcome measurements can be explained in a classical manner, while the results of some three-outcome measurements cannot. This points to the important role of the number of outcomes in revealing the nonclassicality hidden in a quantum system. Moreover, our methods allow us to improve the understanding of quantum correlations by delivering novel criteria for quantum steering and improved ways to construct local hidden variable models.