We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb-which describes all transformations achievable by a given quantum network-and link product-the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view-based on connections of elementary circuits-and from an axiomatic one-based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.
We sketch a group-theoretical framework, based on the Heisenberg-Weyl group, encompassing both quantum and classical statistical descriptions of mechanical systems. We re-define in group-theoretical terms the kinematical arena and the state-space of the system, achieving a unified quantum-classical language and a novel version of the correspondence principle. We briefly discuss the structure of observables and dynamics within our framework.
In this paper we introduce a quantum information theoretical model for quantum secret sharing schemes. We show that quantum information theory provides a unifying framework for the study of these schemes. We prove that the information theoretical requirements for a class of quantum secret sharing schemes reduce to only one requirement (the recoverability condition) as a consequence of the no-cloning principle. We give also a shorter proof of the fact that the size of the shares in a quantum secret sharing scheme must be at least as large as the secret itself.
Information-Theoretical restrictions on the information transfer are applied to Quantum Measurements. For the measurement of quantum object S by information system O this restrictions are calculated in Algebraic QM formalism as the inference map to the (sub)algebra of O observables.
A theorem is proved which states that no classical key generating protocol could ever be provably secure. Consequently, candidates for provably secure protocols must rely on some quantum effect. Theorem relies on the fact that BB84 Quantum key distribution protocol has been proven secure.
It is explained how the unification of resonance and decay phenomena into a consistent mathematical theory leads to quantum mechanical time-asymmetry. This provides the theoretical basis for a subsequent paper II in which the interpretation and experimental demonstration of this time-asymmetry is discussed.
An information theoretical model for quantum secret sharing was introduced by A. C. A. Nascimento et al.[Quantum Inf. Comput. Vol.5,1,205,68-79(2003)], which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analy…
The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.
Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum information to any other node at a constant rate independent of the distance between qubits. The physical limits of quantum state transfer in this network are theoretically analyzed, including the effects of disorder, decoherence, and higher-order couplings.
We theoretically compared quantum noise squeezing differences between silicon and graphene nanoresonators based on experimental structure parameters. The conditions to achieve squeezed states of silicon and graphene have been discussed. According to our theoretical analysis, graphene nanoresonators can obtain a much smaller squeezing factor than silicon, taking advantage of their thin thickness. Both the quantum noise and thermal noise (Brownian motion) of typical monolayer graphene nanoresonator can be reduced by 12.58 dB at T = 5 K with a pump voltage of 5 V.
A theoretical quantum key distribution scheme using EPR pairs is presented. This scheme is efficient in that it uses all EPR pairs in distributing the key except those chosen for checking eavesdroppers. The high capacity is achieved because each EPR pair carries 2 bits of key code.
Correlations are a very important tool in the study of multipartite systems, both for classical and quantum ones. The discussion about the quantum nature of correlations permeates Physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Here we provide a short review about the quantum nature of correlations, discussing both its theoretical and experimental aspects. We focus on quantum discord and related measures. After discussing their fundamental aspects (theoretically and experimentally), we proceed by analysing the dynamical behaviour of corr…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such multiparameter estimation can be achieved depends on understanding the many subtleties that come into play: establishing solid foundations is key to delivering future technology for this task. In this article we discuss the state of the art of quantum multiparameter estimation, with a particular emphasis on its theoretical tools, on application to imaging problem…
An observable effects a schematization of the Quantum event structure by correlating Boolean algebras picked by measurements with the Borel algebra of the real line. In a well-defined sense Boolean observables play the role of coordinatizing objects in the Quantum world, by picking Boolean figures and subsequently opening Boolean windows for the perception of the latter, interpreted as local measurement charts. A mathematical scheme for the implementation of this thesis is being proposed based on Category theoretical methods. The scheme leads to a manifold representation of Quantum structure i…
Ghost imaging is a method to nonlocally image an object by transmitting pairs of entangled photons through the object and a reference optical system respectively. We present a theoretical analysis of the quantum noise in this imaging technique. The dependence of the noise on the properties of the apertures in the imaging system are discussed and demonstrated with a numerical example. For a given source, the resolution and the signal-to-noise ratio cannot be improved at the same time .
In this paper it was proved that the quantum relative entropy $D(σ\| ρ)$ can be asymptotically attained by Kullback Leibler divergences of probabilities given by a certain sequence of POVMs. The sequence of POVMs depends on $ρ$, but is independent of the choice of $σ$.
Quantum secret sharing (QSS) schemes without entanglement have huge advantages in scalability and are easier to realize as they only require sequential communications of a single quantum system. However, these schemes often come with drawbacks such as exact ($n, n$) structure, security flaws and absences of effective cheating detections. To address these problems, we propose a verifiable framework by utilizing entanglement-free states to construct ($t, n$)-QSS schemes. Our work is the heuristic step towards information-theoretical security in entanglement-free QSS, and it sheds light on how to…
In this work we propose a novel numerical approach to decompose general quantum programs in terms of single- and two-qubit quantum gates with a $CNOT$ gate count very close to the current theoretical lower bounds. In particular, it turns out that $15$ and $63$ $CNOT$ gates are sufficient to decompose a general $3$- and $4$-qubit unitary, respectively, with high numerical accuracy. Our approach is based on a sequential optimization of parameters related to the single-qubit rotation gates involved in a pre-designed quantum circuit used for the decomposition. In addition, the algorithm can be ado…
This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with $O_{h}$ symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh-Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions . We show how to obtain suitable symmetry-adapted basis sets.
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.
Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to further justifying the group-theoretical method, the problem is first studied from the viewpoint of classical mechanics. Then the radial probability densities predicted by classical mechanics are compared with those predicted from solutions of the problem obtained by the group-theoretical method. The comparisons clearly indicate the convergence of predictions of…
We derive the quantum stochastic master equation for bosonic systems without measurement theory but control theory. It is shown that the quantum effect of the measurement can be represented as the correlation between dynamical and measurement noise. The transfer function representation allows us to analyze a dynamical uncertainty relation which imposes strong constraints on the dynamics of the linear quantum systems. In particular, quantum systems preserving the minimum uncertainty are uniquely determined. For large spin systems, it is shown that local dynamics are equivalent to bosonic system…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel one can define different classical capacities depending on the character of resources applied for encoding and decoding procedures and on the type of information sources. It is shown that for Bernoulli sources the entanglement-assisted classical capacity, which is the largest one, is bounded from above by the quantum dynamical entropy defined in terms of op…
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems theoretical perspective and applied to the formulation of quantum gates. Then quantum systems are defined by introducing feedback to the gates. In Part III, quantum gates and systems are reformulated from a quantum field theoretical perspective using S-matrices. We also discuss how gauge fields are related to feedback.
We have theoretically and experimentally address the possible tandem electro-optical modulator configurations that can be employed to implement Frequency Coded Quantum Key Distribution systems (FC-QKD). A closed and general formulation of the end to end field propagation in a dispersion compensated FC-QKD optical fiber system under the low modulation index regime is presented which accounts for all the possible tandem combinations. The properties and the parameter selection of the modulators to achieve each one are summarized. We also address which protocol (B92, BB84 or either) is feasible to…
We present a theoretical result, which is based on the linear algebra theory (similar operators). The obtained theoretical results optimize the experimental technique to construct quantum computer e.g., reduces the number of steps to perform the logical CNOT (XOR) operation. The present theoretical technique can also be generalized to the other operators in in quantum computation and information theory.
The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete measurement. The optimization theory for the setup is based on the new theoretical approach of quantum combs.
The efficient certification of classically intractable quantum devices has been a central research question for some time. However, to observe a "quantum advantage", it is believed that one does not need to build a large scale universal quantum computer, a task which has proven extremely challenging. Intermediate quantum models that are easier to implement, but which also exhibit this quantum advantage over classical computers, have been proposed. In this work, we present a certification technique for such a sub-universal quantum server which only performs commuting gates and requires very lim…
We apply the quantum Lax-Phillips scattering theory to a relativistically covariant quantum field theoretical form of the (soluble) Lee model. We construct the translation representations with the help of the wave operators, and show that the resulting Lax-Phillips $S$-matrix is an inner function (the Lax-Phillips theory is essentially a theory of translation invariant subspaces). We then discuss the non-relativistic limit of this theory, and show that the resulting kinematic relations coincide with the conditions required for the Galilean description of a decaying system.
In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the quantum counting with the depolarizing channel. We also implement two circuits for the quantum counting -- the ascending-order circuit and the descending-order circuit -- by reversing ordering of application of controlled-Grover operations. By theoretical and numerical calculations for probability distributions, we reveal the difference of probability distribution…
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing. In this paper we give a brief overview of our work on hypersensitivity to perturbation in classical and quantum systems.
{We point out some obstacles raised by the lost of symmetry against the extension to the case of an interacting particle of the approach that {\sl deductively} establishes the Quantum Theory of a free particle according to the group theoretical methods worked out by Bargmann, Mackey and Wigner. Then we develop an approach which overcomes these difficulties in the non relativistic case. According to our approach the different specific forms of the wave equation of an interacting particle are implied by particular first order invariance properties that characterize the interaction with respect t…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that an operator corresponds to the rate of the proper time and that the operator contains terms which oscillate with a very high frequency. We deduce, as an effect of these terms, the existence of an interference between the magnetic field and the rate of proper time. There is a possibility that the conclusion derived in this letter has some implications for astrophysics.
The BB84 and B92 protocols based on polarization coding are usually used in free-space quantum key distribution. Polarization tracking technique is one of the key techniques in the satellite quantum key distribution. Because the photon polarization state will be changed as a result of the satellite movement, both the transmitter and receiver need to have the ability to track the polarization orientation variation to accomplish the quantum cryptography protocols. In this paper, the polarization tracking principles are analyzed based on Faraday effect and the half-wave plate. The transforms of s…
We propose a theoretical framework to quantitatively describe Physical Unclonable Functions (PUFs), including extensions to quantum protocols, so-called Quantum Readout PUFs (QR-PUFs). (QR-) PUFs are physical systems with challenge-response behavior intended to be hard to clone or simulate. Their use has been proposed in several cryptographic protocols, with particular emphasis on authentication. Here, we provide theoretical assumptions and definitions behind the intuitive ideas of (QR-) PUFs. This allows to quantitatively characterize the security of such devices in cryptographic protocols. F…
We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum inf…
Quantum logic operations can be implemented using nonlinear phase shifts (the Kerr effect) or the quantum Zeno effect based on strong two-photon absorption. Both approaches utilize three-level atoms, where the upper level is tuned on resonance for the Zeno gates and off-resonance for the nonlinear phase gates. The performance of nonlinear phase gates and Zeno gates are compared under conditions where the parameters of the resonant cavities and three-level atoms are the same in both cases. It is found that the expected performance is comparable for the two approaches, despite the apparent diffe…
Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. Relaxation of the …
Recently, an information theoretical model for Quantum Secret Sharing (QSS) schemes was introduced. By using this model, we prove that pure state Quantum Threshold Schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the Monotone Span Program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation.
Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures. Calculating partial trace becomes computationally very intensive with increasing number of qubits as the Hilbert space dimension increases exponentially. In this paper we discuss about our new method of partial tracing which is based on set theory and it is more efficient. The proposed method of partial tracing overcomes all the limitations of the other well kno…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented sistematically for the first time. A new, dynamics-statistical interpretation of the quantum mechanics is introduced. A particle-wave duality picture incorporated in the wave function through its phase and amplitude is considered.
The Quantum Cheshire Cat (QCC) is an effect introduced recently within the Weak Measurements framework. The main feature of the QCC effect is that a property of a quantum particle appears to be spatially separated from its position. The status of this effect has however remained unclear, as claims of experimental observation of the QCC have been disputed by strong criticism of the experimental as well as the theoretical aspects of the effect. In this paper we clarify in what precise sense the QCC can be regarded as an unambiguous consequence of the standard quantum mechanical formalism applied…
Observers restricted to the observation of pointer states of apparatus cannot conclusively demonstrate that the pointer of an apparatus A registers the state of a system of interest S without perturbing S. Observers cannot, therefore, conclusively demonstrate that the states of a system S are redundantly encoded by pointer states of multiple independent apparatus without destroying the redundancy of encoding. The redundancy of encoding required by quantum Darwinism must, therefore, be assumed from outside the quantum-mechanical formalism and without the possibility of experimental demonstratio…
The absence of a common framework for benchmarking quantum networks is an obstacle to comparing the capabilities of different quantum networks. We propose a general framework for quantifying the performance of a quantum network, which is based on the value created by connecting users through quantum channels. In this framework, we define the quantum network utility metric $U_{QN}$ to capture the social and economic value of quantum networks. While the quantum network utility captures a variety of applications from secure communications to distributed sensing, we study the example of distribute…
We review our recent work addressing various theoretical issues in spin-based quantum dot quantum computation and quantum information processing. In particular, we summarize our calculation of electron exchange interaction in two-electron double quantum dots and multi-electron double dots, and discuss the physical implication of our results. We also discuss possible errors and how they can be corrected in spin-based quantum dot quantum computation. We critically assess the constraints and conditions required for building spin-based solid state quantum dot quantum computers.
The torque density per unit height exerted on a perfectly conducting wedge due to the quantum vacuum fluctuations (the Casimir torque) is obtained. A canonical quantum field theoretical approach with the method of calculating vacuum-to-vacuum propagator (Green function) [1] is used.
A theoretical analysis is presented showing that fundamental complementarity between the particle-like properties of an exciton confined in a semiconductor quantum dot and the ability of the same system to show interference may be studied in a time domain interference experiment, similar to those currently performed. The feasibility of such an experiment, including required pulse parameters and the dephasing effect of the environment, is studied.
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically time-varying coin both numerically and analytically, in order to explore the controllability of quantum walks while preserving its random nature.
Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum rela…
An alternative model to describe the electronic and thermal properties of quantum dot based on triangle geometry is proposed. The model predicts characteristics and limitations of the system by controlling the magnetic field and temperature, and the other parameters involved.
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information theoretically secure fully homomorphic encryption. Here we show, via an information localisation argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required.
Use of non-classical light in a quantum illumination scheme provides an advantage over classical illumination when used for LIDAR with a simple and realistic detection scheme based on Geiger-mode single photon detectors. Here we provide an analysis that accounts for the additional information gained when detectors do not fire that is typically neglected and show an improvement in performance of quantum illumination. Moreover, we provide a theoretical framework quantifying performance of both quantum and classical illumination for simple target detection, showing parameters for which a quantum …
Quantum random walks (QRWs) are random processes in which the resulting probability density of the "walker" state, whose movement is governed by a "coin" state, is described in a non-classical manner. Previously, Q-plates have been used to demonstrate QRWs with polarization and orbital angular momentum playing the role of coin and walker states, respectively. In this theoretical analysis, we show how stress-engineered optics can be used to develop new platforms for complex QRWs through relative simple optical elements. Our work opens up new paths to speed up classical-to-quantum transitions in…
The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal system to study the nonequilibrium dynamics in isolated quantum systems, triggering intensive recent theoretical endeavors on this fundamental …
Thermodynamics originated in the need to understand novel technologies developed by the Industrial Revolution. However, over the centuries the description of engines, refrigerators, thermal accelerators, and heaters has become so abstract that a direct application of the universal statements to real-life devices is everything but straight forward. The recent, rapid development of quantum thermodynamics has taken a similar trajectory, and, e.g., "quantum engines" have become a widely studied concept in theoretical research. However, if the newly unveiled laws of nature are to be useful, we need…
In our review we focus on the quantum spin liquid, defining the thermodynamic, transport and relaxation properties of geometrically frustrated magnets (insulators) represented by herbertsmithite $\rm ZnCu_{3}(OH)_6Cl_2$.
