Single-emitter quantum key distribution over 175 km of fibre with optimised finite key rates.

Quantum key distribution with solid-state single-photon emitters is gaining traction due to their rapidly improving performance and compatibility with future quantum networks. Here we emulate a quantum key distribution scheme with quantum-dot-generated single photons frequency-converted to 1550 nm, achieving count rates of 1.6 MHz with [Formula: see text] and asymptotic positive key rates over 175 km of telecom fibre. We show that the commonly used finite-key analysis for non-decoy state QKD drastically overestimates secure key acquisition times due to overly loose bounds on statistical fluctuations. Using the tighter multiplicative Chernoff bound to constrain the estimated finite key parameters, we reduce the required number of received signals by a factor 108. The resulting finite key rate approaches the asymptotic limit at all achievable distances in acquisition times of one hour, and at 100 km we generate finite keys at 13 kbps for one minute of acquisition. This result is an important step towards long-distance single-emitter quantum networking.

Quantum Hilbert Hotel.

In 1924 David Hilbert conceived a paradoxical tale involving a hotel with an infinite number of rooms to illustrate some aspects of the mathematical notion of "infinity." In continuous-variable quantum mechanics we routinely make use of infinite state spaces: here we show that such a theoretical apparatus can accommodate an analog of Hilbert's hotel paradox. We devise a protocol that, mimicking what happens to the guests of the hotel, maps the amplitudes of an infinite eigenbasis to twice their original quantum number in a coherent and deterministic manner, producing infinitely many unoccupied levels in the process. We demonstrate the feasibility of the protocol by experimentally realizing it on the orbital angular momentum of a paraxial field. This new non-Gaussian operation may be exploited, for example, for enhancing the sensitivity of NOON states, for increasing the capacity of a channel, or for multiplexing multiple channels into a single one.

Nondemolition measurement of the vacuum state or its complement.

Measurement is integral to quantum information processing and communication; it is how information encoded in the state of a system is transformed into classical signals for further use. In quantum optics, measurements are typically destructive, so that the state is not available afterwards for further steps. Here we show how to measure the presence or absence of the vacuum in a quantum optical field without destroying the state, implementing the ideal projections onto the respective subspaces. This not only enables sequential measurements, useful for quantum communication, but it can also be adapted to create novel states of light via bare raising and lowering operators.

Fidelity and coherence measures from interference.

By utilizing single particle interferometry, the fidelity or coherence of a pair of quantum states is identified with their capacity for interference. We consider processes acting on the internal degree of freedom (e.g., spin or polarization) of the interfering particle, preparing it in states rho_{A} or rho_{B} in the respective path of the interferometer. The maximal visibility depends on the choice of interferometer, as well as the locality or nonlocality of the preparations, but otherwise depends only on the states rho_{A} and rho_{B} and not the individual preparation processes themselves. This allows us to define interferometric measures which probe locality and correlation properties of spatially or temporally separated processes, and can be used to differentiate between processes that cannot be distinguished by direct process tomography using only the internal state of the particle.

Mixed state geometric phases, entangled systems, and local unitary transformations.

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

Observation of geometric phases for mixed states using NMR interferometry.

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well-understood, noiseless, pure-state case.

Interference of quantum channels.

We show how interferometry can be used to characterize certain aspects of general quantum processes and, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, the maximum interference visibility, and the closest unitary operator to a given physical process under this measure.

Direct estimations of linear and nonlinear functionals of a quantum state.

We present a simple quantum network, based on the controlled-SWAP gate, that can extract certain properties of quantum states without recourse to quantum tomography. It can be used as a basic building block for direct quantum estimations of both linear and nonlinear functionals of any density operator. The network has many potential applications ranging from purity tests and eigenvalue estimations to direct characterization of some properties of quantum channels. Experimental realizations of the proposed network are within the reach of quantum technology that is currently being developed.