Faithful exchange of quantum information can in future become a key part of many computational algorithms. Some Authors suggest to use chains of mutually coupled spins as channels for quantum communication. One can divide these proposals into the groups of assisted protocols, which require some additional action from the users, and natural ones, based on the concept of state mirroring. We show that mirror is fundamentally not the feature chains of spins-1/2 coupled by the Heisenberg interaction, but without local magnetic fields. This fact has certain consequences in terms of the natural state transfer.
We derive in the Heisenberg picture a widely used phenomenological coupling element to treat feedback effects in quantum optical platforms. Our derivation is based on a microscopic Hamiltonian, which describes the mirror-emitter dynamics based on a dielectric, a mediating fully quantized electromagnetic field, and a single two-level system in front of the dielectric. The dielectric is modeled as a a system of identical two-state atoms. The Heisenberg equation yields a system of describing differential operator equations, which we solve in the Weisskopf-Wigner limit. Due to a finite round-trip …
We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-…
We prove strictly that one dimension spin 1/2 Heisenberg model has a symmetry of energy spectrum between its subspace $n$ and the subspace $L-n$ of the Fock space. Our proof is completed by introducing two general quantum operations. One is a flip operation of spin direction and another is a mirror reflection of spin sites.
We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of ground-state pairwise entanglement for the four-qubit model by identifying a Z_2 symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.
In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct methods, that by applying periodic quantum error corrections, we can achieve the Heisenberg scaling for an extended period of time on a three-qubit Tavis-Cumming Model, where three two-level atoms interact with a single cavity mode, under certain approximations. The generalization to arbitrary number of atoms case is also discussed.
Information transmission of two qubits through two independent 1D Heisenberg chains as a quantum channel is analyzed. It is found that the entanglement of two spin-$\frac 12$ quantum systems is decreased during teleportation via the thermal mixed state in 1D Heisenberg chain. The entanglement teleportation will be realized if the minimal entanglement of the thermal mixed state is provided in such quantum channel. High average fidelity of teleportation with values larger than 2/3 is obtained when the temperature {\it T} is very low. The mutual information $\mathcal{I}$ of the quantum channel de…
Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we study the attainability of strong, global notions of Heisenberg scaling in the fundamental problem of phase estimation, from a practical standpoint. A main message of this work is an asymptotic noise "threshold" for global Heisenberg scaling. We first demonstrate that Heisenberg scaling is fragile to noises in the sense that it cannot be achieved in the presence of phase damping noi…
Using the adaptive time-dependent density-matrix renormalization group method, the dynamics of entanglement and quantum discord of a one-dimensional spin-1/2 XXZ chain is studied when anisotropic interaction quenches are applied at different temperatures. The dynamics of the quantum discord and pairwise entanglement between the nearest qubits shows that the entanglement and quantum discord will first oscillate and then approach to a constant value. The quantum discord can be used to predict the quantum phase transition, while the entanglement cannot.
Spin-spin interactions generated by a detuned cavity are a standard mechanism for generating highly entangled spin squeezed states. We show here how introducing a weak detuned parametric (two-photon) drive on the cavity provides a powerful means for controlling the form of the induced interactions. Without a drive, the induced interactions cannot generate Heisenberg-limited spin squeezing, but a weak optimized drive gives rise to an ideal two-axis twist interaction and Heisenberg-limited squeezing. Parametric driving is also advantageous in regimes limited by dissipation, and enables an altern…
Many promising ideas for quantum computing demand the experimental ability to directly switch 'on' and 'off' a physical coupling between the component qubits. This is typically the key difficulty in implementation, and precludes quantum computation in generic solid state systems, where interactions between the constituents are 'always on'. Here we show that quantum computation is possible in strongly coupled (Heisenberg) systems even when the interaction cannot be controlled. The modest ability of 'tuning' the transition energies of individual qubits proves to be sufficient, with a suitable en…
Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with the increase of the temperature. The DM interaction can lead to a higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will be the maximum…
In this comment we show that the experimental results for a universally valid uncertainty relation in ref.[J. Erhart et al. Nat. Phys.(2012)10.1038/nphys2194]cannot be justified. The experiments cannot be recognized to establish a violation of the Heisenberg-type uncertainty relation suggested by Ozawa[Phys. Lett. A318(2003)21, Phys. Rev. A67(2003)042105].
It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer's reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer's reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.
We study quantum frequency estimation for $N$ qubits subjected to independent Markovian noise, via strategies based on time-continuous monitoring of the environment. Both physical intuition and an extended convexity property of the quantum Fisher information (QFI) suggest that these strategies are more effective than the standard ones based on the measurement of the unconditional state after the noisy evolution. Here we focus on initial GHZ states and on parallel or transverse noise. For parallel noise, i.e. dephasing, we show that perfectly efficient time-continuous photo-detection allows to …
The global-state fidelity cannot characterize those quantum phase transitions (QPTs) induced by continuous level crossing due to its collapse around each crossing point. In this paper, we take the isotropic Lipkin-Meshkov-Glick (LMG) model and the antiferromagnetic one-dimensional Heisenberg model as examples to show that the partial-state fidelity can signal such level-crossing QPTs. Extending to the thermodynamic limit we introduce the partial-state fidelity susceptibility and study its scaling behavior. The maximum of the partial-state fidelity susceptibility goes like $N$ for the LMG model…
We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function, and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bou…
We present some exact results for the optimal Matrix Product State (MPS) approximation to the ground state of the infinite isotropic Heisenberg spin-1/2 chain. Our approach is based on the systematic use of Schmidt decompositions to reduce the problem of approximating for the ground state of a spin chain to an analytical minimization. This allows to show that results of standard simulations, e.g. density matrix renormalization group and infinite time evolving block decimation, do correspond to the result obtained by this minimization strategy and, thus, both methods deliver optimal MPS with th…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible, they cannot be jointly performed. We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations. Taking this correspondence relationship as a bridge, we incorporate Heisenberg's uncertainty principle into quantum multiparameter es…
We describe an algebra G of diagrams which faithfully gives a diagrammatic representation of the structures of both the Heisenberg-Weyl algebra H - the associative algebra of the creation and annihilation operators of quantum mechanics - and U(L_H), the enveloping algebra of the Heisenberg Lie algebra L_H. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also mirrored in the structure of U(L_H). While both H and U(L_H) are images of G, the algebra G has a richer structure and therefore embodies a finer combinatorial realization of the creation-annihilation…
In this paper we ask a common psychological question and provide a physics answer: "Looking into a mirror can one get entangled with one's image?" This is not a frivolous question; rather, it bears on the effect of boundaries on the behavior of quantum entanglement between a harmonic oscillator and a quantum field, a basic problem of interest in proposed mirror-field superposition and related experiments in macroscopic quantum phenomena, as well as atomic fluctuation forces near a conducting surface. The object's internal degree of freedom is modeled by a harmonic oscillator and the presence o…
In this paper we present a model for the kinematics and dynamics of optomechanics which describe the coupling between an optical field, here modeled by a massless scalar field, and the internal (e.g., determining its reflectivity) and mechanical (e.g., displacement) degrees of freedom of a moveable mirror. As opposed to implementing boundary conditions on the field we highlight the internal dynamics of the mirror which provides added flexibility to describe a variety of setups relevant to current experiments. The inclusion of the internal degrees of freedom in this model allows for a variety o…
In this paper we analyze an exactly solvable model consisting of an inertial Unruh-DeWitt detector which interacts linearly with a massless quantum field in Minkowski spacetime with a perfectly reflecting flat plane boundary. Firstly a set of coupled equations for the detector's and the field's Heisenberg operators are derived. Then we introduce the linear entropy as a measure of entanglement between the detector and the quantum field under mirror reflection, and solve the early-time detector-field entanglement dynamics. After coarse-graining the field, the dynamics of the detector's internal …
Finding the ground state energy of the Heisenberg Hamiltonian is an important problem in the field of condensed matter physics. In some configurations, such as the antiferromagnetic translationally-invariant case on the 2D square lattice, its exact ground state energy is still unknown. We show that finding the ground state energy of the Heisenberg model cannot be an NP-Hard problem unless P=NP. We prove this result using a reduction to a sparse set and certain theorems from computational complexity theory. The result hints at the potential tractability of the problem and encourages further res…
We consider the motion of the end mirror of a cavity in whose standing wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this backaction of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the backaction of…
