Sequential random access codes and self-testing of quantum measurement instruments

Abstract

Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transformmeasure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.Subsequently, we apply our results to self-test a quantum instrument. is the task of inferring physical entities (states, channels, measurements) solely from correlations produced in experiments i.e. identifying the unique physical entities that are compatible with observed data. Self-testing is typically studied in Bell experiments where notably methods for self-testing quantum instruments have been developed [15,16]. Recently however, self-testing was introduced in the broad scope of prepare-and-measure scenarios [10], and was further developed using QRACs to robustly self-test both preparations and measurements [10][11][12]. Notably however, prepare-and-measure scenarios do not enable self-tests of general quantum operations. In particular, it does not enable self-tests of quantum instruments since the quantum system after the measurement is irrelevant to the outcome statistics produced in the experiment. We show that our prepare-transform-measure scenario overcomes this conceptual limitation. We find that optimal pairs of sequential QRACs self-test quantum instruments. However, such optimal correlations require idealised (noiseless) scenarios which are never the case in a practical implementation. Therefore, we also show how sequential QRACs allow for inference of noise-robust bounds on the sharpness parameter in a quantum instrument. This is makes our results applicable to experimental demonstrations. Finally, we discuss relevant generalisations of our results. New J. Phys. 21 (2019) 083034 K Mohan et al

Experimental test of sequential weak measurements for certified quantum randomness extraction

“…Recently, it has been exploited for sequential protocols, in which a system undergoes multiple measurements without ever completely collapsing or losing its useful quantum features, which can be harvested repeatedly. In this manner, Bell inequalities can be violated more times [36][37][38][39][40], quantum random access codes can be used by two parties [41,42], and quantum instruments can be tested [43]. More important for this work is using weak measurements to produce random bits from the same physical system repeatedly [44,45].…”

Noise-robust preparation contextuality shared between any number of observers via unsharp measurements

“…This has also been experimentally demonstrated [10,11]. Moreover, shared quantum correlations have recently also been studied in other tasks such as entanglement witnessing [12], quantum steering [13,14] and a semidevice-independent setting [15][16][17][18].…”

Weak form of self-testing

“…Self-testing is an active research field and a particularly interesting direction is to explore its powers and limitations by deriving new types of self-testing statements or impossibility results. For instance we have recently learned that one can self-test quantum channels [49], entangled measurements [50,51], and quantum instruments [52], or that one can extend the concept of self-testing to prepare-and-measure scenarios [53][54][55][56][57][58]. In this work we derive a new type of self-testing statement which allows us to certify the state but not the measurements.…”