Unconditionally Secure Bit Commitment by Transmitting Measurement Outcomes

We propose a new unconditionally secure bit commitment scheme based on Minkowski causality and the properties of quantum information. The receiving party sends a number of randomly chosen BB84 qubits to the committer at a given point in space-time. The committer carries out measurements in one of the two BB84 bases, depending on the committed bit value, and transmits the outcomes securely at light speed in opposite directions to remote agents. These agents unveil the bit by returning the outcomes to adjacent agents of the receiver. The security proofs rely only on simple properties of quantum information and the impossibility of superluminal signalling.Comment: Discussion expanded pedagogically in response to referee comment

Device-Independent Relativistic Quantum Bit Commitment

We examine the possibility of device-independent relativistic quantum bit commitment. We note the potential threat of {\it location attacks}, in which the behaviour of untrusted devices used in relativistic quantum cryptography depends on their space-time location. We describe relativistic quantum bit commitment schemes that are immune to these attacks, and show that these schemes offer device-independent security against hypothetical post-quantum adversaries subject only to the no-signalling principle. We compare a relativistic classical bit commitment scheme with similar features, and note some possible advantages of the quantum schemes

Quantum paradox of choice: More freedom makes summoning a quantum state harder

The properties of quantum information in space-time can be investigated by studying operational tasks. In one such task, summoning, an unknown quantum state is supplied at one point, and a call is made at another for it to be returned at a third. Hayden-May recently proved necessary and sufficient conditions for guaranteeing successful return of a summoned state for finite sets of call and return points when there is a guarantee of at most one summons. We prove necessary and sufficient conditions when there may be several possible summonses and complying with any one constitutes success. We show there is a "quantum paradox of choice" in summoning: the extra freedom in completing the task makes it strictly harder. This intriguing result has practical applications for distributed quantum computing and cryptography and also implications for our understanding of relativistic quantum information and its localization in space-time.This work was partially supported by an FQXi grant and by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society

A scheme for performing strong and weak sequential measurements of non-commuting observables

Quantum systems usually travel a multitude of different paths when evolving through time from an initial to a final state. In general, the possible paths will depend on the future and past boundary conditions, as well as the system's dynamics. We present a gedanken experiment where a single system apparently follows mutually exclusive paths simultaneously, each with probability one, depending on which measurement was performed. This experiment involves the measurement of observables that do not correspond to Hermitian operators. Our main result is a scheme for measuring these operators. The scheme is based on the erasure protocol [Phys. Rev. Lett. 116, 070404 (2016), arXiv:1409.1575] and allows a wide range of sequential measurements at both the weak and strong limits. At the weak limit the back action of the measurement cannot be used to account for the surprising behavior and the resulting weak values provide a consistent yet strange account of the system's past.Comment: Similar to published version, Quantum Studies: Mathematics and Foundations (2016). arXiv admin note: text overlap with arXiv:1409.157