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arXiv:quant-ph/0605080

When the Left Hand and the Right Hand Cooperate Without Informing their Owner

Dodson, Brian

Published May 8, 2006• 0 citations
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Abstract

A specific instantiation of classical correlation from entangled quantum resources can be established at a distance through the use of local measurements without classical communication. It is thereby possible to, e.g., allow distant entities to randomly combine forces on a course of action which is an element of a predetermined set of possible actions. When this protocol is used, no one knows which action has been chosen. The protocol is intrinsically secure in the same sense as a one-time pad. The entities must have a shared entanglement resource, be able to measure that resource in a predetermined reference frame, and know what they must do to carry out all of the possible actions.

DOI
10.48550/arxiv.quant-ph/0605080

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A specific instantiation of classical correlation from entangled quantum resources can be established at a distance through the use of local measurements without classical communication. It is thereby possible to, e.g., allow distant entities to randomly combine forces on a course of action which is an element of a predetermined set of possible actions. When this protocol is used, no one knows which action has been chosen. The protocol is intrinsically secure in the same sense as a one-time pad. The entities must have a shared entanglement resource, be able to measure that resource in a predetermined reference frame, and know what they must do to carry out all of the possible actions.
The experimental detection of multipartite entanglement usually requires a number of appropriately chosen local quantum measurements that are aligned with respect to a previously shared common reference frame. The latter, however, can be a challenging prerequisite, e.g., for satellite-based photonic quantum communication, making the development of alternative detection strategies desirable. One possibility for avoiding the distribution of classical reference frames is to perform a number of local measurements with settings distributed uniformly at random. In this Letter, we follow such a treatment and show that an improved detection and characterization of multipartite entanglement is possible by combining statistical moments of different order. To do so, we make use of designs that are pseudorandom processes allowing us to link the present entanglement criteria to ordinary reference frame independent ones. The strengths of our methods are illustrated in various cases, starting with two qubits and followed by more involved multipartite scenarios.
Abstract Two or more particles which have interacted in the past, may in general maintain nontrivial quantum mechanical correlations, described by non-factorized wave functions. These correlations, under optimal conditions, can manifest themselves no matter how far they travel away from each other and even when the separate parts cannot dynamically influence each other, leading to apparently paradoxical situations. These correlations are known as quantum entanglement. However counter-intuitive and surprising it may sometimes look, it is rather one of the more beautiful and experimentally well established predictions of quantum mechanics.
This paper studies information-theoretically secure quantum homomorphic encryption (QHE) schemes of classical data. Previous works on information-theoretically secure QHE schemes (like Childs'05, Liang'13, and others) are typically based on the Quantum-One-Time-Pad (QOTP) approach of Ambainis et al. [AMTdW'00]. There, the encryption of a bit is a qubit, randomly selected from a set of four possible qubits. This paper takes a different approach and presents the RBE (Random-Basis Encryption) scheme -- a QHE scheme in which the encryption of a bit is a qubit, randomly selected from a set of an immense number of qubits. Second, this paper studies weak measurements (WM) and presents a WM-based attack on legacy QOTP-based Quantum Key Distribution (QKD) protocols. Then, we use the RBE scheme to construct a QKD protocol and argue that this protocol is resilient to such WM-based attacks. Finally, this paper raises the following question. Entanglement is an essential resource in quantum information and quantum computation research. Hence, once generated, how can its owner secure entangled systems of qubits? We inspect possible QOTP-based solutions, suggest an RBE-based solution, and discuss some of the benefits of the latter.
Multipartite nonlocality is of great fundamental interest and constitutes a useful resource for many quantum information protocols. However, demonstrating it in practice, by violating a Bell inequality, can be difficult. In particular, standard experimental setups require the alignment of distant parties' reference frames, which can be challenging or impossible in practice. In this work we study the violation of certain Bell inequalities, namely the Mermin, Mermin-Klyshko, and Svetlichny inequalities, without shared reference frames, when parties share a Greenberger-Horne-Zeilinger state. Furthermore, we analyze how these violations demonstrate genuine multipartite features of entanglement and nonlocality. For three, four, and five parties, we show that it is possible to violate these inequalities with high probability, when the parties choose their measurements from the three Pauli operators, defined only with respect to their local frames. Moreover, the probability of violation, and the amount of violation, are increased when each party chooses their measurements from the four operators describing the vertices of a tetrahedron. We also consider how many randomly chosen measurement directions are needed to violate the Bell inequalities with high probability. We see that the obtained levels of violation are sufficient to also demonstrate genuine multipartite entanglement and nonseparability. Finally, we show analytically that choosing from two measurement settings per party is sufficient to demonstrate the maximum degree of genuine multipartite entanglement and nonseparability with certainty when the parties' reference frames are aligned in one direction so that they differ only in rotations around one axis.