Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.

Geometric Property of Off Resonance Error Robust Composite Pulse

The precision of quantum operations is affected by unavoidable systematic errors. A composite pulse (CP), which has been well investigated in nuclear magnetic resonance (NMR), is a technique that suppresses the influence of systematic errors by replacing a single operation with a sequence of operations. In NMR, there are two typical systematic errors, Pulse Length Error (PLE) and Off Resonance Error (ORE). Recently, it was found that PLE robust CPs have a clear geometric property. In this study, we show that ORE robust CPs also have a simple geometric property, which is associated with trajectories on the Bloch sphere of the corresponding operations. We discuss the geometric property of ORE robust CPs using two examples.

On the induced metric of a photon qubit for different points of action in Bloch sphere

Travelling with harmonical actions about the referential line, the moment the photon qubit emits form the atom as a packet, not only embedded by the envelopes of quadratic nature overlap but also by the non-quadratic overlap effect as well in concurrent. This paper followed on by the subsistence of both ways of overlapping, focuses mainly on the induced metric of photon qubit, which concluded to be in 3-sphere by the local parameterization so called as Hopf coordinates. The protruded photon qubit in the induced Riemannian metric, for different points of the Bloch sphere, are in a manner that the stereographic projection of volume enveloped in 3-sphere determines the circular geometry in 2-sphere with the cross-sectional function in perpendicular to the continuum line of travel.

Emulation of Ternary and Quaternary Logic Quantum Computers By 2-Dimensional Analog Signal Processing

In this paper, a novel method for the emulation of qutrit and ququart based quantum computers is proposed. The Hilbert space and Bloch sphere representations of qutrits are initially discussed, preceding the emulation of a single qutrit using a classical system. The signal representing the state of the quantum system is defined as the sum of quadrature and in-phase 2-dimensional space-varying signals, which represent the basis states of the quantum system. Focus is mainly conferred on the frequency-domain representation of the signal, due to an innate bijective mapping found between the dimensions in the Hilbert space and the frequencies of the signal. An m -qutrit addressing scheme is then proposed which is used in the application of quantum ternary gates and measurement operations. The proposed theory is then used to simulate a ternary version of the Deutsch-Jozsa algorithm on MATLAB. This paper also includes a section on the extension of the theory to the case of ququarts. It concludes with a brief introduction to a potential system for emulation, and lists algorithms that can be implemented on the proposed system.

Effects of frequency detuning and excitation quantum number on the dynamics of entanglement in the Jaynes-Cummings polariton model

We present a scheme for generating polaritons which are maximally entangled qubit states in the Jaynes-Cummings interaction mechanism. Considering a specific case of an atom initially in an excited state entering a cavity mode initially in vacuum state and in a non-resonant atom-field Jaynes-Cummings interaction, we demonstrate using graphical representation on the Bloch sphere that an increase in frequency detuning leads to an increase in Rabi oscillations. Analysis of the dynamical behaviour of quantum entanglement in the general Jaynes-Cummings atom-field interactions measured by concurrence show that frequency detuning and photon number parameters are vital in enhancing entanglement.

There and back again: A circuit extraction tale

Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for one-way computations allowing measurements in three different planes of the Bloch sphere, most research so far has focused on computations containing only measurements in the XY-plane. Here, we give the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow. The algorithm is efficient and the resulting circuits do not contain ancillae. One-way computations are represented using the ZX-calculus, hence the algorithm also represents the most general known procedure for extracting circuits from ZX-diagrams. In developing this algorithm, we generalise several concepts and results previously known for computations containing only XY-plane measurements. We bring together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus. These rules are used to simplify measurement patterns by reducing the number of qubits while preserving both the semantics and the existence of gflow. The results can be applied to circuit optimisation by translating circuits to patterns and back again.

Superconductor Qubits Hamiltonian Approximations Effect on Quantum State Evolution and Control

Quantum state on Bloch sphere for superconducting charge qubit, phase qubit and flux qubit for all time in absence of external drive is stable to initial state. By driving the qubits, approximation of charge and flux Hamiltonian lead to quantum state rotation in Bloch sphere around an axis completely differ from rotation vector of exact Hamiltonian. The trajectory of quantum state for phase qubit for approximated and exact Hamiltonian is the same but the expectation of quantum observable has considerable errors as two other qubits. microwave drive control is designed for approximated Hamiltonian and exerted on actual systems and shows completely different trajectory with respect to desired trajectory. Finally a nonlinear control with external µV voltage control and nA current control is designed for general qubit which completely stabilizes quantum state toward a desired state.

Quantum Cognitive Triad: Semantic Geometry of Context Representation

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory.