Quantum Bounds for Temporal Correlations

Costantino Budroni

Chun-Wang Wu, Man-Chao Zhang, Yanli Zhou +11 more

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.

Shin-Liang Chen, Jens Eisert

We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints-for which we prove genuine quantum separations over local hidden variable models-or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, and bounding the maximum successful probability in quantum randomness access codes.

Michael J. W. Hall

Marcin L Nowakowski

In this paper, we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiates them from spatial quantum correlations. With a growing interest in the representation of quantum states as topological objects, we consider quantum history bundles based on the temporal manifold and show the source of the violation of monogamous temporal Bell-like inequalities. We introduce definitions for the mixture of quantum histories and consider their entanglement as sections over the Hilbert vector bundles. As a generalization of temporal Bell-like inequalities, we derive the quantum bound for multi-time Bell-like inequalities.

Lê Phuc Thinh