Cloning of a quantum measurement

We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1 -> 2 learning of the measurement, otherwise the task is called 1 -> 2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension of the Hilbert space. For 1 -> 2 cloning we also propose a simple quantum network that realizes the optimal strategy.Comment: 10 pages, 1 figur

Memory cost of quantum protocols

In this paper we consider the problem of minimizing the ancillary systems required to realize an arbitrary strategy of a quantum protocol, with the assistance of classical memory. For this purpose we introduce the notion of memory cost of a strategy, which measures the resources required in terms of ancillary dimension. We provide a condition for the cost to be equal to a given value, and we use this result to evaluate the cost in some special cases. As an example we show that any covariant protocol for the cloning of a unitary transformation requires at most one ancillary qubit. We also prove that the memory cost has to be determined globally, and cannot be calculated by optimizing the resources independently at each step of the strategy.Comment: 9 page

Quantum learning algorithms for quantum measurements

We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information.Comment: 13 pages, 2 figure

Unambiguous comparison of quantum measurements

The goal of comparison is to reveal the difference of compared objects as fast and reliably as possible. In this paper we formulate and investigate the unambiguous comparison of unknown quantum measurements represented by non-degenerate sharp POVMs. We distinguish between measurement devices with apriori labeled and unlabeled outcomes. In both cases we can unambiguously conclude only that the measurements are different. For the labeled case it is sufficient to use each unknown measurement only once and the average conditional success probability decreases with the Hilbert space dimension as 1/d. If the outcomes of the apparatuses are not labeled, then the problem is more complicated. We analyze the case of two-dimensional Hilbert space. In this case single shot comparison is impossible and each measurement device must be used (at least) twice. The optimal test state in the two-shots scenario gives the average conditional success probability 3/4. Interestingly, the optimal experiment detects unambiguously the difference with nonvanishing probability for any pair of observables.Comment: 10 pages, 1 figur