Quantum Information Processing

In this paper, we present two new ways of quantum synchronization coding based on the $$(\varvec{u}+\varvec{v}|\varvec{u}-\varvec{v})$$ construction and the product construction, respectively, and greatly enrich the varieties of available quantum synchronizable codes. The circumstances where the maximum synchronization error tolerance can be reached are explained for both constructions. Furthermore, repeated-root cyclic codes derived from the $$(\varvec{u}+\varvec{v}|\varvec{u}-\varvec{v})$$ construction are shown to be able to provide better Pauli error-correcting capability than BCH codes.

Starting from an association scheme induced by a finite group and the corresponding Bose–Mesner algebra, we construct quantum Markov chains, their entangled versions, using the quantum probabilistic approach. Our constructions are based on the intersection numbers and their duals Krein parameters of the schemes. We make the connection for the first time between the fusion rules of anyonic particles evolving on a 2D surface to the Krein parameters of an association scheme. We consider braid group $$B_3$$ that describes the unitary dynamics of the anyons as the automorphism subgroup of the graphs. The dynamics induced by the fusions (and the adjoint splitting operations) may be viewed as the chain evolving on a growing graph and the braiding as automorphisms on a fixed graph. In our quantum probability framework, infinite iterations of the unitaries, which can encode algorithmic content for quantum simulations, can describe asymptotics elegantly if the particles are allowed to evolve coherently for a longer period. We define quantum states on the Bose–Mesner algebra which is also a von Neumann algebra as well as a Frobenius algebra to build the quantum Markov chains providing yet another perspective to topological computation, whereas frameworks such as Unitary Modular Categories can identify and characterize new anyonic systems our framework can build upon them within quantum probabilistic framework that are suitable for asymptotic analysis.

We study two-level q-deformed angular momentum states, and using q-deformed harmonic oscillators, we provide a framework for constructing qubits and quantum gates. We also present the construction of some basic one-qubit and two-qubit quantum logic gates.

A violation of a Bell inequality can formally be expressed as a witness for quantum nonlocality. A new four-qubit Bell inequality is optimally violated by $$\chi $$ -type entangled state, but not by four-qubit GHZ, W and cluster state. Hence, $$\chi $$ -type entangled state is a good candidate to implement simultaneous dense coding. In this paper, we propose a simultaneous dense coding protocol with genuine four-particle entangled state, $$\chi $$ -type entangled state, in which two receivers can simultaneously obtain their respective classical information sent by a sender. The double controlled-NOT operator, which is used as the locking operator, play a crucial role in our protocol. The security of simultaneous dense coding is analyzed against the intercept-resend attack. The preparation of $$\chi $$ -type entangled state has been studied in various physics systems, and it has been experimentally generated with nearly deterministic scheme and high generation rate. Thus, our protocol is feasible with the current experimental technology.

In this paper, we propose a protocol of joint remote state preparation of an equatorial two-qubit pure quantum state using GHZ states, performing projective measurements and appropriate unitary operations. The probability of success of our scheme is shown to increase if one of the parties holding the partial information transmits the information classically to the receiver.

Device and semi-device-independent private quantum randomness generators are crucial for applications requiring private randomness. However, they are vulnerable to detection inefficiency attacks and this limits severely their usage for practical purposes. Here, we present a method for protecting semi-device-independent private quantum randomness generators in prepare-and-measure scenarios against detection inefficiency attacks. The key idea is the introduction of a blocking device that adds failures in the communication between the preparation and measurement devices. We prove that, for any detection efficiency, there is a blocking rate that provides protection against these attacks. We experimentally demonstrate the generation of private randomness using weak coherent states and standard avalanche photo-detectors.

Enhanced precision measurements using entangled many particle states are crucial for their technological applications in quantum information science and metrology. Squeezed spin states are a class of permutation symmetric N particle entangled states, which exhibit reduced quantum fluctuation in their collective spin angular momentum in a certain direction, and they are useful for quantum enhanced metrology. Permutation symmetric states attract attention as they offer significant test grounds for the description of entanglement in multipartite quantum systems, which is crucial for processing complex quantum information tasks. Spin squeezing serves as an experimentally amenable collective criterion of entanglement in symmetric multiqubit systems. In this paper, we explore spin-squeezing behavior in different classes of N-qubit symmetric states consisting of all permutations of two distinct spinors. We employ Majorana geometric representation of multiqubit states obeying exchange symmetry for this purpose. We prove that N qubit symmetric states consisting of two distinct non-orthogonal spinors do exhibit spin squeezing, thus expanding the avenues of their applicability in quantum enhanced sensing tasks.