A quantum statistical approach to simplified stock markets

We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the portfolio of a certain trader to a different one. This computation can also be carried out using some kind of Feynman graphs adapted to the present context.     

Measurement-Based Quantum Computation and Undecidable Logic

We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power of (classical) formal logic languages defined on the underlying mathematical graphs. In particular, we show that for all graph state resources which can yield a computational speed-up with respect to classical computation, the underlying graphs—describing the quantum correlations of the states—are associated with undecidable logic theories. Here undecidability is to be interpreted in a sense similar to Gödel’s incompleteness results, meaning that there exist propositions, expressible in the above classical formal logic, which cannot be proven or disproven.     

Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions

Boundary correlation functions of the six and nineteen vertex models on an N×N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by the use of the quantum inverse scattering method. For the nineteen vertex model, the boundary correlation functions are shown to be expressed in terms of those for the six vertex model.     

From Schrödinger’s equation to the quantum search algorithm

The quantum search algorithm is a technique for searching N possibilities in only O(√N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrödinger’s equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.     

A Proposal of Telecloning for a Three-Particle Entangled?W?State

A 1→2 telecloning solution for an arbitrary three-particle entangled W state is proposed in which two four-particle entangled states are used as quantum channels. It is proposed that the three-particle W state can be telecloned based on the quantum teleportation and the local copying of entanglement, and the fidelity of each clone depends on the input state. This scheme can be generalized into the case of 1→N (N>2) telecloning of an arbitrary three-particle W state. Furthermore, another scheme for 1→N (N≥2) telecloning of an arbitrary n-particle (n≥4) W state is proposed, the multi-bit controlled-NOT (CNOT) gates and additional particles are needed in this case. Project 10574060 supported by the National Natural Science Foundation of China.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

Polynomial invariants for SU(2) monopoles

We present an explicit expression for the topological invariants associated to SU(2) monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in terms of Seiberg-Witten invariants. In this analysis we use recent exact results on the moduli space of vacua of the untwisted N = 1 and N = 2 supersymmetric counterparts of the topological quantum field theory under consideration, as well as on electric-magnetic duality for N = 2 supersymmetric gauge theories.     

Implementtion of a Computation Algorithm for Deutsch-Jozsa Problem Utilizing Spatial Distribution of Photons

Several implementations of quantum computation making effective use of the quantum behavior of single-photons have been explored. These implementing methods were found unsuitble for large-scale computation, because they require 2^N-1 optical paths to represent N qubits. In this paper, a new computing scheme is described which utilizes spatial distribution of photons. The occupation of several optical paths by single-photons is adopted as qubits. This adoption gives several extension of processing capacity and computational functionality with a simple setup. An optical implementation of a solution algorithm on four-bit Deutsch-Jozsa problem is demonstrated with utilization of the spatial distribution of photons.     

Secure quantum sealed-bid auction with post-confirmation

A new secure quantum auction with post-confirmation is proposed, which is a direct application of the multi-particle super dense coding scheme to the auction problem. In this scheme all bidders use M groups n-particle GHZ states to represent their bids. Different from classical auction protocols and the previous secure quantum sealed-bid auction protocols, in the present scheme, by introducing a post-confirmation mechanism the honesty of the quantum sealed-bid auction is guaranteed, i.e., malicious bidders cannot collude with auctioneers. Also by sharing secret keys with the bidders the auctioneer could insure the anonymity of the bidders.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Nekrasov prepotential with fundamental matter from the quantum spin chain

Nekrasov functions were conjectured in Mironov and Morozov (2009) [1] to be related to exact Bohr-Sommerfeld periods of quantum integrable systems. This statement was thoroughly checked for the case of the pure SU(Nc) gauge theory in Mironov and Morozov (2009) [2] and Popolitov (2010) [3]. Here we successfully perform a set of checks in the case of gauge group SU(Nc) with additional Nf fundamental hypermultiplets. We show that the Baxter equation for the spin chain gives the same quantum periods as the one for the Gaudin system in this case.     

二阶量子路径的相干控制

研究了有_N个中间能级连接初态和目标态的情况下量子路径的控制策略．以_N=3的量子体系为例,详细阐述了针对弱的宽频场的4_N分块控制方案,其中分块的边界频率依赖于量子体系的共振频率．此策略利用了路径幅度中共振和非共振项的相干效应,可通过只调节2_N个相位变量实现．     

Quantum steganography with large payload based on entanglement swapping of χ-type entangled states

In this paper, we firstly propose a new simple method to calculate entanglement swapping of χ-type entangled states, and then present a novel quantum steganography protocol with large payload. The new protocol adopts entanglement swapping to build up the hidden channel within quantum secure direct communication with χ-type entangled states for securely transmitting secret messages. Comparing with the previous quantum steganographies, the capacity of the hidden channel is much higher, which is increased to eight bits. Meanwhile, due to the quantum uncertainty theorem and the no-cloning theorem its imperceptibility is proved to be great in the analysis, and its security is also analyzed in detail, which is proved that intercept-resend attack, measurement-resend attack, ancilla attack, man-in-the-middle attack or even Dos(Denial of Service) attack couldn't threaten it. As a result, the protocol can be applied in various fields of quantum communication.     

Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.     

Modeling and simulation of efficiency droop in GaN-based blue light-emitting diodes incorporating the effect of reduced active volume of InGaN quantum wells

The efficiency droop of InGaN-based blue light-emitting diodes (LEDs) is analyzed using numerical simulations with a modified ABC carrier recombination model. The ABC model is modified to include the effect of reduced effective active volume of InGaN quantum wells (QWs) and incorporated into the numerical simulation program. It is found that the droop of internal quantum efficiency (IQE) can be well explained by the effect of reduced light-emitting active volume without assuming a large Auger recombination coefficient. A simulated IQE curve with the modified ABC model is found to fit quite well with a measured efficiency curve of an InGaN LED sample when the effective active volume takes only 2.5% of the physical volume of QWs. The proposed numerical simulation model incorporating the reduced effective active volume can be advantageous for use in the modeling and simulation of InGaN LEDs for higher efficiency.     

A short impossibility proof of quantum bit commitment

Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment–bindingness tradeoff (Lo and Chau, 1997 [1], Mayers, 1997 [2]). A strengthened and explicit impossibility proof has been given in D?Ariano et al. (2007) [3] in the Heisenberg picture and in a C^?${\mathrm{C}}^{?}$-algebraic framework, considering all conceivable protocols in which both classical and quantum information is exchanged. In the present Letter we provide a new impossibility proof in the Schrödinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs (Chiribella et al., 2008 [4]), with each single-party strategy represented by a conditioned comb. We prove that assuming a stronger notion of concealment—for each classical communication history, not in average—allows Alice?s cheat to pass also the worst-case Bob?s test. The present approach allows us to restate the concealment–bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with the metric given by the comb discriminability-distance.     

Probing spin entanglement by gate-voltage-controlled interference of current correlation in quantum spin Hall insulators

We propose an entanglement detector composed of two quantum spin Hall insulators and a side gate deposited on one of the edge channels. For an ac gate voltage, the differential noise contributed from the entangled electron pairs exhibits the nontrivial step structures, from which the spin entanglement concurrence can be easily obtained. The possible spin dephasing effects in the quantum spin Hall insulators are also included.     

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.