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.

We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas in the pure state case when a system undergoes noncyclic and unitary quantum evolution.

Concerted efforts are underway to establish an infrastructure for a global quantum Internet to realise a spectrum of quantum technologies. This will enable more precise sensors, secure communications, and faster data processing. Quantum communications are a front‐runner with quantum networks already implemented in several metropolitan areas. A number of recent proposals have modelled the use of space segments to overcome range limitations of purely terrestrial networks. Rapid progress in the design of quantum devices have enabled their deployment in space for in‐orbit demonstrations. We review developments in this emerging area of space‐based quantum technologies and provide a roadmap of key milestones towards a complete, global quantum networked landscape. Small satellites hold increasing promise to provide a cost effective coverage required to realise the quantum Internet. The state of art in small satellite missions is reviewed and the most current in‐field demonstrations of quantum cryptography are collated. The important challenges in space quantum technologies that must be overcome and recent efforts to mitigate their effects are summarised. A perspective on future developments that would improve the performance of space quantum communications is included. The authors conclude with a discussion on fundamental physics experiments that could take advantage of a global, space‐based quantum network.

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.

Global-scale quantum communication links will form the backbone of the quantum internet. However, exponential loss in optical fibres precludes any realistic application beyond few hundred kilometres. Quantum repeaters and space-based systems offer solutions to overcome this limitation. Here, we analyse the use of quantum memory (QM)-equipped satellites for quantum communication focussing on global range repeaters and memory-assisted (MA-) QKD, where QMs help increase the key rate by synchronising otherwise probabilistic detection events. We demonstrate that satellites equipped with QMs provide three orders of magnitude faster entanglement distribution rates than existing protocols based on fibre-based repeaters or space systems without QMs. We analyse how entanglement distribution performance depends on memory characteristics, determine benchmarks to assess the performance of different tasks and propose various architectures for light-matter interfaces. Our work provides a roadmap to realise unconditionally secure quantum communications over global distances with near-term technologies.