Unitary Interaction Research Articles

Unitary interaction geometries in few-body systems

Unitary interaction geometries in few-body systems

On the Probabilistic Quantum Error Correction

Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the error-correcting procedure for general noise. We generalized the Knill-Laflamme conditions for probabilistically correctable errors. We show that for some noise channels, we should encode the information into a mixed state to maximize the probability of successful error correction. Finally, we investigate an advantage of the probabilistic error-correcting procedure over the deterministic one. Reducing the probability of successful error correction allows for correcting errors generated by a broader class of noise channels. Significantly, if the errors are caused by a unitary interaction with an auxiliary qubit system, we can probabilistically restore a qubit state by using only one additional physical qubit.

Quantum correlations beyond entanglement between two moving atoms interacting with a coherent cavity

Studying the ability of atom-photon interactions, especially in two two-level atomic systems, to generate quantum information resources has recently become an important research topic in quantum information science. Therefore, this paper explores the ability of two moving atoms coupling with a coherent field through a two-photon transition to generate atomic quantum correlations by using local quantum uncertainty (LQU), local quantum Fisher information (LQFI) as well as logarithmic negativity (LN). Schrödinger equation is used to obtain the time evolution of the atom-cavity-atom interactions with an initial coherent cavity state and an initial atomic uncorrelated pure state. The generation of atomic LQU, LQFI, and LN correlations are exactly examined under the unitary interaction parameter effects, including the atom-cavity coupling strengths, the cavity field half-wave number, and the initial coherent state intensity. The atom-cavity-atom interaction parameters lead to notable changes in the amplitudes, speed, and regularity of the LQU, LQFI, and LN dynamics, which can be enhanced by increasing the initial coherent intensity. The cavity field half-wave number leads to generating atomic quantum correlations with regular oscillatory behavior. The sudden death-birth phenomenon of the logarithmic negativity depends on the atom-cavity-atom interaction and the atomic location parameter.

Quantum measurements constrained by the third law of thermodynamics

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements -- and are hence all ruled out by the third law in such a case -- and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently "unsharp".

Macroscopic delayed choice and retrocausality: Quantum eraser, Leggett-Garg, and dimension witness tests with cat states

We propose delayed choice experiments carried out with macroscopic qubits, realised as macroscopically-distinct coherent states $|\alpha\rangle$ and $|-\alpha\rangle$. Quantum superpositions of $|\alpha\rangle$ and $|-\alpha\rangle$ are created via a unitary interaction $U(\theta)$ based on a nonlinear Hamiltonian. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality (MrC). We therefore consider weak macroscopic realism (wMR), which specifies a hidden variable $\lambda_{\theta}$ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting $\phi$. Using entangled states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by $\lambda_{\theta}$ without specification of the state at the level of $\hbar$, where fringes manifest. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the dimension witness inequality applied to the Wheeler-Chaves-Lemos-Pienaar experiment, where measurements need only distinguish the macroscopic qubit states. This negates all two-dimensional non-retrocausal models, thereby suggesting MrC. However, one can interpret consistently with wMR, thus avoiding MrC, by noting extra dimensions, and by noting that the violations require further unitary dynamics $U$ for each system. The violations are then explained as failure of deterministic macroscopic realism (dMR), which specifies validity of $\lambda_{\theta}$ prior to the dynamics $U(\theta)$ determining the measurement setting $\theta$. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate EPR paradoxes at a microscopic level.

Capacities of Gaussian Quantum Channels With Passive Environment Assistance

Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders). Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions. In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas. Concerning classical communication, we prove a general coding theorem for the classical capacity under and energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

Conformal symmetry in nuclear structure

The purpose of this paper is to introduce the unitary limit as applied in systems of cold atoms into collective states of heavy and even-even nuclei and to identify a related physical example. This is accompanied by the determination of observables of conformal symmetry in nuclear structure. A Hamiltonian is defined that governs the scattering process of an incident pair of two slow neutrons onto a heavy, even-even target nucleus in the framework of the Interacting Boson Model of nuclear structure. A unitary pair-collective state interaction is introduced along with the effective range expansion for a pair-collective state scattering length. The solutions to the coupled channels equations provide a scattering state for the two neutrons that couples with an intermediate state of the A+2n compound nucleus. The unitary limit manifests itself when the intermediate states correspond to pair-collective state resonances the positions of which coincide with the energies of IBM states of the closed channels. The position and the width of each resonance is measurable via the fluctuation of the cross section which tunes the pair-collective state scattering length. Conformal symmetry is represented in a tower of equally spaced states that emerges at the unitary limit from two-boson excitations on the IBM state of the closed channel. These tower states are measurable as a regularity pattern of fluctuations of the cross section, in terms of regular positions and widths. The manifestation of the unitary limit and conformal symmetry via fluctuations of the cross section indicates the A+2n compound nucleus as a physical laboratory for the examination of the BCS-BEC crossover, of an underlying critical point and of algebras with infinite number of generators.

Multilevel quantum thermodynamic swap engines

We study energetic exchanges and fluctuations in two-stroke quantum thermodynamic engines where the working fluid is represented by two multilevel quantum systems, i.e. qudits, the heat flow is allowed by relaxation with two thermal reservoirs at different temperatures, and the work exchange is operated by a partial-swap unitary interaction. We identify three regimes of operation (heat engine, refrigerator, and thermal accelerator), present the thermodynamic uncertainty relations between the entropy production and the signal-to-noise ratio of work and heat, and derive the full joint probability of the stochastic work and heat. Our results bridge the gap between two-qubit and two-mode bosonic swap engines, and show which properties are maintained (e.g., a non fluctuating Otto efficiency) and which are lost for increasing dimension (e.g., small violations of the standard thermodynamic uncertainty relations or the possibility of beating the Curzon-Ahlborn efficiency).

Nonclassical atomic system dynamics time-dependently interacts with finite entangled pair coherent parametric converter cavity fields

We consider a time-dependent model that describes a qubit time-dependently interacting with a cavity containing finite entangled pair coherent parametric converter fields. The dynamics of some quantum phenomena, as: phase space information, quantum entanglement and squeezing, are explored by atomic Husimi function, atomic Wehrl entropy, variance, and entropy squeezing. The influences of the unitary qubit-cavity interaction, the difference between the two-mode photon numbers, the initial atomic coherence, and the time-dependent qubit location are investigated. It is found that the regularity, the amplitudes and the frequency of the quantum phenomena can be controlled by the physical parameters. For the initial atomic pure state, the qubit-cavity entanglement, the qubit phase space information, and atomic squeezing can be generated strongly compared to those of the initial atomic mixed state. The time-dependent location parameters enhance the generated quantum phenomena, and their effect can be enhanced by the parameters of the two-mode photon numbers and the initial atomic coherence.

Thermodynamic uncertainty relations for bosonic Otto engines.

We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperatures after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations, and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.

No Purification Ontology, No Quantum Paradoxes

It is almost universally believed that in quantum theory the two following statements hold: (1) all transformations are achieved by a unitary interaction followed by a von-Neumann measurement; (2) all mixed states are marginals of pure entangled states. I name this doctrine the dogma of purification ontology. The source of the dogma is the original von Neumann axiomatisation of the theory, which largely relies on the Schrődinger equation as a postulate, which holds in a nonrelativistic context, and whose operator version holds only in free quantum field theory, but no longer in the interacting theory. In the present paper I prove that both ontologies of unitarity and state-purity are unfalsifiable, even in principle, and therefore axiomatically spurious. I propose instead a minimal four-postulate axiomatisation: (1) associate a Hilbert space {mathcal {H}}_text{A} to each systemtext{A}; (2) compose two systems by the tensor product rule {mathcal {H}}_{text{A}text{B}}={mathcal {H}}_text{A}otimes {mathcal {H}}_text{B}; (3) associate a transformation from system text{A} to text{B} to a quantum operation, i.e. to a completely positive trace-non-increasing map between the trace-class operators of text{A} and text{B}; (4) (Born rule) evaluate all joint probabilities through that of a special type of quantum operation: the state preparation. I then conclude that quantum paradoxes—such as the Schroedinger-cat’s, and, most relevantly, the information paradox—are originated only by the dogma of purification ontology, and they are no longer paradoxes of the theory in the minimal formulation. For the same reason, most interpretations of the theory (e.g. many-world, relational, Darwinism, transactional, von Neumann–Wigner, time-symmetric,...) interpret the same dogma, not the strict theory stripped of the spurious postulates.

Quantum Secret Sharing Protocol Using Maximally Entangled Multi-qudit States

The purpose of this paper is to develop a (N − k) threshold quantum secret sharing (QSS) scheme by using entangled multi-qudit states shared between N qudits such that (k ≤ N − k). We introduce first multi-qudit separable states of a Hilbert space associated with a disconnected multi-qudit system. The entangled multi-qudit states are obtained from disconnected states by means of a unitary interaction operator governing the evolution of the multi-qudit system, where the pairwise interaction establishes links between qudits. The generated entangled states are chosen to be maximally entangled with respect to a specific bi-partition ( $A_{2} \bigcup A_{1} $ ) with k = |A2|≤|A1| = (N − k) of the whole system such that the von Neumann entropy $S(\rho _{A_{2}})$ is maximal. The maximally entanglement property with respect to the splitting ( $A_{2} \bigcup A_{1} $ ) of this N-qudit entangled states will be used by a dealer (D) to share an encoded quantum secret with (N − 1) other players, such that at least the (N − k) specified players belonging to A1 have to cooperate jointly to get the complete information about the secret.

Effect of Stark shift on nonlocal correlation of two atoms in a cavity containing a parametric amplifier and a Kerr like medium

An analytical solution is obtained for a system consisting of two atoms interacting with a nondegenerate parametric amplifier of a cavity field containing a Kerr like medium in the presence of Stark shift terms. The nonlinearity of the interaction leads to the generation of different nonlocal correlations (NLCs) beyond entanglement concurrence, which are measured by uncertainty-induced quantum nonlocality and maximal Bell’s function. It is found that the generation of the NLCs, due to the atom-cavity unitary interaction, can be controlled by the nonlinearity of the Kerr like medium and the Stark shift. The Kerr like medium and the Stark shift lead to reduce the regularity and the amount of the generated nonlocal correlations. The reduction in the generated nonlocal correlations, due to the Kerr like medium, is increased by the increase in the Stark shift parameter and vice versa.

Quantum dynamics of a qutrit in a cavity filled with Kerr-like medium and intrinsic noise

We study the dynamics of the intrinsic noise (IN) model of a three-level atom (qutrit) in V-configuration. The qutrit is inside an open cavity with a Kerr-like medium. The quantifiers of the atomic population, entanglement and mixedness are evaluated under the physical parameters of the photon multiplicity, IN and the nonlinearity of both the unitary interaction and the Kerr-like medium. It is found that the generated entanglement and mixedness may be enhanced by filling the cavity with a nonlinear medium. The transfer of the energy between the two upper states and the lower state are very sensitive to the physical parameters. The entanglement and mixedness depend on the initial coherent intensity, the IN and the Kerr-like medium.

Dynamics of quantum coherence and entanglement in an intrinsic noise model of a V-type qutrit system interacting with a coherent field

An analytical solution of the dynamical evolution of an intrinsic noise model of a V-type three-level atom confined in a cavity having one-mode coherent field via multi-photon transitions is obtained. We investigate the effect of the physical parameters of the qutrit-cavity unitary interaction, the intrinsic noise and the photon multiplicity, on important quantum effects such as: the atomic inversion, the quantum coherence, the entanglement and the total correlation. These physical parameters control the phenomenon of the collapses and revivals, and the regularity of the oscillatory behavior of the atomic-inversion. When the intrinsic noise is considered, the dynamics of the entropy, the negativity and the mutual information are different, while the entropy grows, the entanglement negativity and the mutual information degrades to their stationary values. It is found that the quantum coherence, the entanglement, the total correlation and their stationary values are very sensitive to any change in the physical parameters.

Trace distance discord and Bell-function correlations beyond entanglement in two SC-qubits interacting with a dissipative SC-cavity

An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.

Quantum speed limit constraints on a nanoscale autonomous refrigerator.

Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, however, have attracted a great deal of attention in the past few years. In this paper, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a tradeoff relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called "bounding second order cooling rate" and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second-order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second-order cooling rate. We study the efficiency of the refrigerator at maximum bounding second-order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second-order cooling rate is given by a simple formula resembling the Curzon-Ahlborn relation.

Solutions of a Two-Particle Interacting Quantum Walk.

We study the solutions of an interacting Fermionic cellular automaton which is the analogue of the Thirring model with both space and time discrete. We present a derivation of the two-particle solutions of the automaton recently in the literature, which exploits the symmetries of the evolution operator. In the two-particle sector, the evolution operator is given by the sequence of two steps, the first one corresponding to a unitary interaction activated by two-particle excitation at the same site, and the second one to two independent one-dimensional Dirac quantum walks. The interaction step can be regarded as the discrete-time version of the interacting term of some Hamiltonian integrable system, such as the Hubbard or the Thirring model. The present automaton exhibits scattering solutions with nontrivial momentum transfer, jumping between different regions of the Brillouin zone that can be interpreted as Fermion-doubled particles, in stark contrast with the customary momentum-exchange of the one-dimensional Hamiltonian systems. A further difference compared to the Hamiltonian model is that there exist bound states for every value of the total momentum and of the coupling constant. Even in the special case of vanishing coupling, the walk manifests bound states, for finitely many isolated values of the total momentum. As a complement to the analytical derivations we show numerical simulations of the interacting evolution.

Phase space information in a non-linear quantum system containing a Kerr-like medium through Su(1, 1)-algebraic treatment

Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.

Classical capacities of quantum channels with environment assistance

A quantum channel physically is a unitary interaction between the information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [Karumanchi et al., arXiv[quant-ph]:1407.8160], we consider a benevolent third party, i.e. a helper, controlling the environment state, and how the helper's presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, indeed two variants, one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, the two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.