Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced here the compatible information measures, respectively. A sketch of an information optimization of a quantum experimental setup is proposed.
The expectation values of a hermitean operator A in (2s+1)(2s+1) specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other (2s+1)(2s+1) coherent states also provide a basis for self-adjoint operators. This is proven by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system.
I consider the interaction of a superposition of mesoscopic coherent states and its approach to a mixed state as a result of a suitably controlled environment. I show how the presence of a gain medium in a cavity can lead to diagonalization in coherent state basis in contrast to the standard model of decoherence. I further show how the new model of decoherence can lead to the generation of $s$ ordered quasi distributions.
Quantum entanglement generation is generally known to be impossible by any classical means. According to Poisson statistics, coherent photons are not considered quantum particles due to the bunching phenomenon. Recently, a coherence approach has been applied to interpret quantum features such as the Hong-Ou-Mandel (HOM) effect, Franson-type nonlocal correlation, and delayed-choice quantum eraser, where the quantum feature is due to basis-product superposition at the cost of 50 % photon loss. For this, it has been understood that a fixed sum-phase relation between paired photons is the bedrock …
The random switching of measurement bases is commonly assumed to be a necessary step of quantum key distribution protocols. In this paper we show that switching is not required for coherent state continuous variable quantum key distribution. We show this via the no-switching protocol which results in higher information rates and a simpler experimental setup. We propose an optimal eavesdropping attack against this protocol, for individual Gaussian attacks, and we investigate and compare the no-switching protocol applied to the original BB84 scheme.
The Bell basis, a set of maximally entangled biphoton state, is a critical prerequisite towards quantum information processing, and many quantum applications have highlighted the requirement for the manipulation of high-dimensional Bell basis. While the Bell states can be created by using ingenious single-photon quantum gates, its implementation complexity in higher dimensions is significantly increased. Here we present an elaborate approach to show that the adaptive pump modulation enable the efficient preparation of Bell basis in arbitrary-dimensional Hilbert space. A complete set of four-di…
The strange property of the Einstein-Podolsky-Rosen (EPR) correlation between two remote physical systems is a primitive object on the study of quantum entanglement. In order to understand the entanglement in canonical continuous-variable systems, a pair of the EPR-like uncertainties is an essential tool. Here, we consider a normalized pair of the EPR-like uncertainties and introduce a state-overlap to a classically correlated mixture of coherent states. The separable condition associated with this state-overlap determines the strength of the EPR-like correlation on a coherent-state basis in o…
The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is the maximal mixture of stabilizer codewords. In the code basis, the output density matrix is diagonal, the joint output of the system and the auxiliary is block diagonal. The coherent information is worked out by counting the weights of error operators.
We introduce graph state basis diagonalization to calculate the coherent information of a quantum code passing through a Pauli channel. The scheme is 5000 times faster than the best known one for some concatenated repetition codes, providing us a practical constructive way of approaching the quantum capacity of a Pauli channel. The calculation of the coherent information of non-additive quantum code can also be greatly simplified in graph state basis.
The construction of a class of unitary operators generating linear superpositions of generalized coherent states from the ground state of a quantum harmonic oscillator is reported. Such a construction, based on the properties of a new ad hoc introduced set of hermitian operators, leads to the definition of new basis in the oscillator Hilbert space, extending in a natural way the displaced Fock states basis. The potential development of our method and our results is briefly outlined.
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and non-perturbative approximations already known in the quantum field theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.
We use a single squeezed state to represent a qubit, which can be coherently processed in a deconvolution picture (DP) in the presence of noise. We avail ourselves of the fact that when evolution is governed by a quadratic dissipative equation, there exists a basis of squeezed states that evolves to another basis of such states in the DP. An operator acts as an impurity filter, restoring the coherence lost from the inexorable interactions of the qubit with its surroundings.
We show that the $N$-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of $N$ two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the $N$-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.
Coherent beam combining refers to the process of generating a bright output beam by merging independent input beams with locked relative phases. We report the first quantum mechanical noise limit calculations for coherent beam combining and compare our results to quantum-limited amplification. Our coherent beam combining scheme is based on an optical Fourier transformation which renders the scheme compatible with integrated optics. The scheme can be layed out for an arbitrary number of input beams and approaches the shot noise limit for a large number of inputs.
Glauber-Sudarshan diagonal coherent state P-representation has been used to determine geometric phase for non-classical states of light. For a given density operator $\hat{ρ_1}$ of two mode optical beam, we evolve it in complex projective ray space $(\cal R)$ to $\hat{ρ_2}$ and to $\hat{ρ_3}$ by changing its state of polarisation using unitary operator $\mathrm{\hat{U}_p}(θ)$. The diagonal coherent state basis has been utilized to represent the density operators instead of fock state basis as in the fock state basis the state vector in present work evolve under unitary operator produe infinite…
Electromagnetically induced transparency (EIT) is observed in a three-level system composed of an excited state and two coherent superpositions of the two ground-state levels. This peculiar ground state basis is composed of the so-called bright and dark states of the same atomic system in a standard coherent population trapping configuration. The characteristics of EIT, namely, width of the transmission window and reduced group velocity of light, in this unusual basis, are theoretically and experimentally investigated and are shown to be essentially identical to those of standard EIT in the sa…
We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We first show that the basis states of this system apply a set of nonlinear transformations on the input signals and thus can implement neurons. We then show that the system exhibits a fading memory that can be controlled by its dissipation rates. Finally we show that a strong coupling between the oscillators is important in order to ensure complex dynamics and to …
Dynamics of the sub-Ohmic spin-boson model is investigated by employing a multitude of the Davydov D$_1$ trial states, also known as the multi-D$_1$ Ansatz. Accuracy in dynamics simulations is improved significantly over the single D$_1$ Ansatz, especially in the weak system-bath coupling regime. The reliability of the multi-D$_1$ Ansatz for various coupling strengths and initial conditions are also systematically examined, with results compared closely with those of the hierarchy equations of motion and the path integral Monte Carlo approaches. In addition, a coherent-incoherent phase crossov…
Fast coherent control of a charge qubit on solid neon with a spin-qubit-compatible resonator
RIKEN Center for Quantum Computing（RIKEN量子计算中心）；Institute of Physics, University of Augsburg（奥格斯堡大学物理研究所）；Department of Mechanical Engineering, FAMU-FSU College of Engineering, Florida State University（佛罗里达州立大学FAMU-FSU工程学院机械工程系）；Advanced ICT Research Institute, National Institute of Information and Communications Technology (NICT)（国家信息通信技术研究所高级ICT研究所）；Department of Physics and Astronomy, University of Notre Dame（圣母大学物理与天文学系）；Center for Advanced Analytics and Predictive Sciences, University of Augsburg（奥格斯堡大学先进分析与预测科学中心）；RIKEN Pioneering Research Institute（RIKEN先锋研究所）
By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal set, which we call the pseudo number states, the Morse Hamiltonian is tridiagonal. By using this basis we construct coherent states algebraically for the Morse potential, in a close analogy with the harmonic oscillator. We also show that there exists an unitary displacement operator creating these coherent states from the ground state. We show that our cohere…
We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the `Barut Girardello' coherent states to the Kronecker Product of two non-compact groups.The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of `pair coherent states' rather tha…
We report successful joint operation of quantum and classical communications with shared hardware. Leveraging information learned from the classical DSP, low-noise quantum communications (0.009 SNU at 15 km) compatible with 15 Mbit/s QKD is demonstrated.
We demonstrate a device that allows for the coherent analysis of a pair of optical frequency sidebands in an arbitrary basis. We show that our device is quantum noise limited and hence applications for this scheme may be found in discrete and continuous variable optical quantum information experiments.
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between …
Coherent states provide an appealing method to reconstruct efficiently a pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeroes of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus.…
An extended bosonic coherent basis has been shown by Chen to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space by analyzing the converged values of the ground state energy.
We prove that universal quantum computation can be realized---using only linear optics and $χ^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that $χ^{(2)}$ Hamiltonians and photon-number operators generate the full $\mathfrak{u}(3)$ Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-$Z$ gate can be implemented with only linear optics and $χ…
An extended bosonic coherent basis has been shown by Chen et al to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space and many excited states by analyzing the convergence in the wave functions.
The question of whether sunlight induces coherent dynamics in biological systems is under debate. Here we show, on the basis of an exact fully quantum mechanical treatment, that thermal light induces excited-state coherences in matter similar to those induced by a coherent state. We demonstrate the phenomenon on a V-type model system and a two-state Born-Oppenheimer molecular system. Remarkably, wavepacket-like dynamics is induced in the excited molecular potential-energy surface.
We propose a new way of implementing several elementary quantum gates for qubits in the coherent state basis. The operations are probabilistic and employ single photon subtractions as the driving force. Our schemes for single-qubit phase gate and two-qubit controlled phase gate are capable of achieving arbitrarily large phase shifts with currently available resources, which makes them suitable for the near-future tests of quantum information processing with superposed coherent states.
In this paper, we show that correlated coherent states (CCSs) are the most adequate candidates for the role of quantum analogues of the thermal states. The main result of our study reduces to the fact that quantum thermal effects under conditions of the equilibrium of an object with the stochastic environment at any temperatures can be explained consistently only on the basis of the set of CCSs.
Operational criterion for Wigner function negativity
Università di Genova（热那亚大学）；INFN - Sezione di Genova（意大利国家核物理研究所热那亚分部）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家研究委员会光学研究所）；European Laboratory for Non-linear Spectroscopy, Universitá di Firenze（佛罗伦萨大学欧洲非线性光谱学实验室）
We introduce new sophisticated attacks with a Hong-Ou-Mandel interferometer against quantum key distribution (QKD) and propose a new QKD protocol grafted with random basis shuffling to block up those attacks. When the polarization basis is randomly and independently shuffled by sender and receiver, the new protocol can overcome the attacks even for not-so-weak coherent pulses. We estimate the number of photons to guarantee the security of the protocol.
We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes. This division of proc…
We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased bases (MUB) with possibly different noise intensities affecting each basis. We show that not all pairs of MUB can be used in this construction, and we provide a criterion for determiniing those MUB that actually do yield extremal compatible observables. We apply our criterion to all pairs of Fourier conjugate MUB, and we prove that in this case extremality …
We discuss and implement experimentally a method for characterizing quantum gates operating on superpositions of coherent states. The peculiarity of this encoding of qubits is to work with a non-orthogonal basis, and therefore some technical limitations prevent us from using standard methods, such as process tomography. We adopt a different technique, that relies on some a-priori knowledge about the physics underlying the functioning of the device. A parameter characterizing the global quality of the quantum gate is obtained by \virtually" processing an entangled state.
We discuss what can be inferred from measurements on one- and two-qubit systems using a single measurement basis at various times. We show that, given reasonable physical assumptions, carrying out such measurements at quarter-period intervals is enough to demonstrate coherent oscillations of one or two qubits between the relevant measurement basis states. One can thus infer from such measurements alone that an approximately equal superposition of two measurement basis states has been created in a coherent oscillation experiment. Similarly, one can infer that a near maximally entangled state of…
We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_λ$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical propertie…
The coherent state method has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except $U_q[osp(1|2)]$, one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely $U_q[gl(2|1)]$, in constructing $q$--boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified i…
The efficient storage and on-demand retrieval of quantum optical states that are compatible with the telecommunications C-band is a requirement for future terrestrial-based quantum optical networking. Spectrum in the C-band minimises optical fiber-propagation losses, and broad optical bandwidth facilitates high-speed networking protocols. Here we report on a telecommunication wavelength and bandwidth compatible quantum memory. Using the Off-Resonant Cascaded Absorption protocol in hot $^{87}$Rb vapour, we demonstrate a total memory efficiency of $20.90(1)\,\%$ with a Doppler-limited storage ti…
Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $ρ(H_0)$ the energy shift determines the outgoing state.
We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm that iteratively generates the Krylov basis can be augmented to treat coherent states associated with the Jacobi group, the semi-direct product of the 3-dimensional real Heisenberg-Weyl group $H_{1}$, and the symplectic group, $Sp(2,\mathbb{R})\simeq SU(1,1)$. Such coherent states are physically realized as squeezed states in, for example, quantum optics. W…
Reconciliation is an important step to correct errors in Quantum Key Distribution (QKD). In QKD, after comparing basis, two legitimate parties possess two correlative keys which have some differences and they could obtain identical keys through reconciliation. In this paper, we present a new rate compatible reconciliation scheme based on Row Combining with Edge Variation (RCEV) Low Density Parity Check (LDPC) codes which could change code rate adaptively in noisy channel where error rate may change with time. Our scheme is easy to implement and could get good efficiency compared to existing sc…
The discrimination of coherent states is a key task in optical communication and quantum key distribution protocols. In this work, we use a photon-number-resolving detector, the transition-edge sensor, to discriminate binary-phase-shifted coherent states at a telecom wavelength. Owing to its dynamic range and high efficiency, we achieve a bit error probability that unconditionally exceeds the standard quantum limit (SQL) by up to 7.7 dB. The improvement to the SQL persists for signals containing up to approximately seven photons on average and is achieved in a single shot (i.e. without measure…
The discrimination of two nonorthogonal states is a fundamental element for secure and efficient communication. Quantum measurements of nonorthogonal coherent states can enhance information transfer beyond the limits of conventional technologies. We demonstrate a strategy for binary state discrimination based on optimized single-shot measurements with photon number resolving (PNR) detection with finite number resolution. This strategy enables a high degree of robustness to noise and imperfections while being scalable to high rates and in principle allows for surpassing the quantum noise limit …
Present work is an attempt to compare quantum discord and quantum entanglement of Werner states formed with the four bipartite entangled coherent states (ECS) used recently for quantum teleportation of a qubit encoded in superposed coherent state. Out of these, two based on maximally ECS are exactly similar to the perfect Werner state, while the rest two, based on non-maximally ECS, which are called quasi-Werner states behave in somewhat different ways and their quantum discord and entanglement depends on the coherent amplitude and the measurement basis.
With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we manage to give a compact and coherent account of the various properties of higher-order-Schmidt-representations.
An open question of fundamental importance in thermodynamics is how to describe the fluctuations of work for quantum coherent processes. In the standard approach, based on a projective energy measurement both at the beginning and at the end of the process, the first measurement destroys any initial coherence in the energy basis. Here we seek for extensions of this approach which can possibly account for initially coherent states. We consider all measurement schemes to estimate work and require that (i) the difference of average energy corresponds to average work for closed quantum systems, and…
Electron spins in silicon quantum dots are excellent qubits because they have long coherence times, high gate fidelities, and are compatible with advanced semiconductor manufacturing techniques. The valley degree of freedom, which results from the specific character of the Si band structure, is a unique feature of electrons in Si spin qubits. However, the small difference in energy between different valley levels often poses a challenge for quantum computing in Si. Here, we show that the spin-valley coupling in Si, which enables transitions between states with different spin and valley quantum…
Motivated by Möbius transformation for symmetrical points under the generalized circle in complex plane, the system of symmetrical spin coherent states corresponding to antipodal qubit states is introduced. It implies the maximally entangled spin coherent states basis, which in the limiting cases reduces to the Bell basis. A specific property of our symmetric image coherent states is that they never become unentangled for any value of $ψ$ from complex plane. By the reduced density matrix and the concurrence determinant methods, it is shown that our basis is maximally entangled. In addition we …
A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectivel…
