Certified randomness in quantum physics

The concept of randomness plays an important role in many disciplines. On one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other hand, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions on the devices that are difficult to meet in practice. However, quantum technologies allow for new methods for generating certified randomness. These methods are known as device-independent because do not rely on any modeling of the devices. Here we review the efforts and challenges to design device-independent randomness generators.Comment: 18 pages, 3 figure

Entanglement preserving local thermalization

We investigate whether entanglement can survive the thermalization of subsystems. We present two equivalent formulations of this problem: (1) Can two isolated agents, accessing only pre-shared randomness, locally thermalize arbitrary input states while maintaining some entanglement? (2) Can thermalization with local heat baths, which may be classically correlated but do not exchange information, locally thermalize arbitrary input states while maintaining some entanglement? We answer these questions in the positive at every nonzero temperature and provide bounds on the amount of preserved entanglement. We provide explicit protocols and discuss their thermodynamic interpretation: we suggest that the underlying mechanism is a speed-up of the subsystem thermalization process. We also present extensions to multipartite systems. Our findings show that entanglement can survive locally performed thermalization processes accessing only classical correlations as a resource. They also suggest a broader study of the channel's ability to preserve resources and of the compatibility between global and local dynamics.Comment: 6+7 pages, 1 figure, closed to the published versio

On the structure of a reversible entanglement generating set for tripartite states

We show that Einstein–Podolsky–Rosen–Bohm (EPR) and Greenberger–Horne–Zeilinger–Mermin (GHZ) states can not generate, through local manipulation and in the asymptotic limit, all forms of three–partite pure–state entanglement in a reversible way. The techniques that we use suggest that there may be a connection between this result and the irreversibility that occurs in the asymptotic preparation and distillation of bipartite mixed states

Optimal randomness certification in the quantum steering and prepare-and-measure scenarios

Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the amount of local or global randomness that can be extracted in two scenarios: (i) the quantum steering scenario, where two parties measure a bipartite system in an unknown state but one of them does not trust his measurement apparatus, and (ii) the prepare-and-measure scenario, where additionally the quantum state is known. We use our methods to compute the maximal amount of local and global randomness that can be certified by measuring systems subject to noise and losses and show that local randomness can be certified from a single measurement if and only if the detectors used in the test have detection efficiency higher than 50%.Comment: 11 pages, 6 figures. v2: Published versio

Non-secret correlations can be used to distribute secrecy

A counter-intuitive result in entanglement theory was shown in [PRL 91 037902 (2003)], namely that entanglement can be distributed by sending a separable state through a quantum channel. In this work, following an analogy between the entanglement and secret key distillation scenarios, we derive its classical analog: secrecy can be distributed by sending non-secret correlations through a private channel. This strengthens the close relation between entanglement and secrecy.Comment: 4 page

Self-testing multipartite entangled states through projections onto two systems

Finding ways to test the behaviour of quantum devices is a timely enterprise, especially in the light of the rapid development of quantum technologies. Device-independent self-testing is one desirable approach, as it makes minimal assumptions on the devices being tested. In this work, we address the question of which states can be self-tested. This has been answered recently in the bipartite case [Nat. Comm. 8, 15485 (2017)], while it is largely unexplored in the multipartite case, with only a few scattered results, using a variety of different methods: maximal violation of a Bell inequality, numerical SWAP method, stabilizer self-testing etc. In this work, we investigate a simple, and potentially unifying, approach: combining projections onto two-qubit spaces (projecting parties or degrees of freedom) and then using maximal violation of the tilted CHSH inequalities. This allows to obtain self-testing of Dicke states and partially entangled GHZ states with two measurements per party, and also to recover self-testing of graph states (previously known only through stabilizer methods). Finally, we give the first self-test of a class multipartite qudit states: we generalize the self-testing of partially entangled GHZ states by adapting techniques from [Nat. Comm. 8, 15485 (2017)], and show that all multipartite states which admit a Schmidt decomposition can be self-tested with few measurements.Comment: The title is changed and the presentation is slightly restructure

Optimal randomness certification from one entangled bit

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.Comment: 7 pages, 1 figure, computational details at http://nbviewer.ipython.org/github/peterwittek/ipython-notebooks/blob/master/Optimal%20randomness%20generation%20from%20entangled%20quantum%20states.ipyn