A Quantum Box

Yongjin Jeon, Seungjun Baek, Jongsung Kim

Abstract In this paper, we present a new framework to construct a quantum circuit of S-boxes.We first model the quantum circuits of S-boxes based on the Toffoli and linear layers. We generate vector spaces with the values of qubits used in the linear layers and apply them to find quantum circuits.Our technique find the quantum circuit by matching the vector space's elements to the S-box's input and output, based on the meet-in-the-middle strategy.We applied our technique to 4-bit S-boxes.While existing LIGHTER-R tools only find 4-bit S-boxes circuits that can be implemented with 4 qubits, our tool accomplishes the same with 5 qubits.Our tool also finds reversible quantum circuits of 4-bit S-boxes, which are odd permutations that LIGHTER-R cannot.We expect our technique will become an important step towards finding optimized S-box quantum circuits.

Carolina Moreira Ferrera, Robin Simmons, James Purcell +2 more

Here we introduce the concept of classical input – quantum output (C-Q) non-signalling boxes, a generalisation of the classical input – classical output (C-C) non-signalling boxes. We argue that studying such objects leads to a better understanding of the relation between quantum nonlocality and non-locality beyond quantum mechanics. The main issue discussed in the paper is whether there exist 'genuine' C-Q boxes or all C-Q boxes can be built from objects already known, namely C-C boxes acting on pre-shared entangled quantum particles. We show that large classes of C-Q boxes are non-genuine. In particular, we show that all bi-partite C-Q boxes with outputs that are pure states are non-genuine. We also present various strategies for addressing the general problem, i.e. for multi-partite C-Q boxes which output mixed states, whose answer is still open. Finally, we show that even some very simple non-genuine C-Q boxes require large amounts of C-C nonlocal correlations in order to simulate them.

Jean-Daniel Bancal, Nicolas Gisin

Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum nonlocality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the no-signaling and independence principle. For the case of boxes without inputs, connecting pairs of bipartite sources and producing binary outputs, we prove that the sources and boxes producing local random outputs and maximal two-box correlations, i.e., ${E}_{2}=\sqrt{2}\ensuremath{-}1, {E}_{2}^{o}=1$, are essentially unique.

Amitabha Sen, Sharon Butler