Quantum key distribution using sequential weak values

Wen-Long Ma, Ping Wang, Weng-Hang Leong +1 more

Quantum measurement can be strong or weak, the former being important in readout and initialization of quantum objects and the latter being useful for monitoring and maneuvering quantum evolution. However, the boundary between weak and strong measurement is unclear. Here we show that a phase transition occurs in sequential quantum measurement, which unambiguously separates the weak and strong measurement by a critical value of measurement strength or duration. We formulate the probability distribution of the output of a sequence of quantum measurements as the Boltzmann distribution of an interacting spin model. The measurement results present phase transitions similar to those in the spin model. In particular the sequential commuting positive operator-valued measurement is mapped to a long-range Ising model, and a projective measurement emerges from sequential weak measurements when the strength or the number of measurements becomes above certain critical values, corresponding to the ferromagnetic phase transition of the spin model. This finding sheds insights on sequential quantum measurement, and also provides the theoretical foundation for constructing projective measurements from sequential weak measurements, which have applications in steering the quantum evolution and initializing quantum systems where strong measurement in a single shot is often not possible.

Masahiro Takeoka

Marcos Curty, Kiyoshi Tamaki, Tobias Moroder

We investigate limitations imposed by detector dead times on the performance of sequential attacks against a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. In particular, we analyze sequential attacks based on unambiguous state discrimination of the signal states emitted by the source and we obtain ultimate upper bounds on the maximal distance achievable by a DPS QKD scheme both for the case of calibrated and uncalibrated devices, respectively.

Norbert Lütkenhaus

Salim Salmi, Abdelkrim Khartoch, Lahcen Oughdir +1 more

Hipólito Gómez-Sousa, Marcos Curty

In this paper, we investigate limitations imposed by sequential attacks on the performance of a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. Specifically, we analyze a sequential attack based on optimal unambiguous discrimination of the relative phases between consecutive signal states emitted by the source. We show that this attack can provide tighter upper bounds for the security of a DPS QKD scheme than those derived from sequential attacks where the eavesdropper aims to identify the state of each signal emitted by the source unambiguously.