Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between principal models of computation, namely, computation over the continuum and computation over the integers (Turing computation). Thus we identify a basic problem in QFT, namely Wightman's computation problem for domains of holomorphy, which we call WHOLO. Inspired by the same analytic functions which are central to the famous CPT theorem of QFT, it is possible to obtain a computational complexity structure for QFT and shed new light on certain complexity classes for this problem WHOLO.
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability, while maintaining and defending the validity of Turing computation and the Church-Turing thesis.
The proposal of the optical scheme for holonomic quantum computation is evaluated based on dynamical resolution to the system beyond adiabatic limitation. The time-dependent Schrödinger equation is exactly solved by virtue of the cranking representation and gauge transformation approach. Besides providing rigorous confirmation to holonomies of the geometrical prediction that holds for the ideally adiabatic situation, the dynamical resolution enables one to evaluate elaborately the amplitude of the nonadiabatic deviation, so that the errors induced to the quantum computation can be explicitly e…
Physical theories constrained with local quantum structure and satisfying the no-signalling principle can allow beyond-quantum global states. In a standard Bell experiment, correlations obtained from any such beyond-quantum bipartite state can always be reproduced by quantum states and measurements, suggesting local quantum structure and no-signalling to be the axioms to isolate quantum correlations. In this letter, however, we show that if the Bell experiment is generalized to allow local quantum inputs, then beyond-quantum correlations can be generated by every beyond-quantum state. This giv…
We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We give the details of the algorithm and demonstrate its performance by classical simulations. Two isotopomers of the hydrogen molecule (H$_2$, HT) were chosen as representative examples and calculations of the lowest rotationless vibrational transition energies were simulated.
The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of material systems, is outlined and tentatively applied to some examples.
Combining abstract to laboratory projected quantum states a general analysis of headline quantum phenomena is presented. Standard representation mode is replaced; instead quantum states sustained by elementary material constituents occupy its place. Renouncing to assign leading roles to language originated in classical physics when describing genuine quantum processes, together with sustainment concept most, if not all weirdness associated to Quantum Mechanics vanishes.
We study the effects of localization on quantum state transfer in spin chains. We show how to use quantum error correction and multiple parallel spin chains to send a qubit with high fidelity over arbitrary distances; in particular distances much greater than the localization length of the chain.
Comment on J.Qin et al., Unconditional and Robust Quantum Metrological Advantage beyond N00N States, PRL 130, 070801 (2023) and J.A. H. Nielsen et.al., Deterministic Quantum Phase Estimation beyond N00N States. PRL 130, 123603 (2023)
Quantum reading aims at retrieving classical information stored in an optical memory with low energy and high accuracy by exploiting the inherently quantum properties of light. We provide an optimal Gaussian strategy for quantum reading with phase-shift keying encoding that makes use of squeezed coherent light and homodyne detectors to largely outperform the Standard Quantum Limit, even in the presence of loss. This strategy, being feasible with current quantum optical technology, represents a viable prototype for a highly efficient and reliable quantum-enhanced optical reader.
A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert-Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence…
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble consisting of finite copies of a single probabilistic machine, hence is as powerful as a probabilistic Turing machine (PTM). Then the hypothesis--that is, the SEnM can effectively simulate a general circuit model of QC--is tested by introducing an information-theoretic inequality, named readout inequality. The inequality is satisfied by the SEnM and imposes a cri…
Quantum metrology is studied in the presence of quantum correlation. The quantum correlation measure based on quantum Fisher information enables us to gain a deeper insight on how quantum correlations are instrumental in setting metrological precision. Our analysis shows that not only the entanglement but also the quantum correlation plays important roles to enhance precision in quantum metrology. Even in the absence of entanglement, quantum correlation can be exploited as the resource to beat standard quantum limit and reach Heisenberg limit in metrology. Clearly unraveling the role of quantu…
There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitabl…
Recently, it was shown that quantum steerability is stronger than the bound set by the instrumental causal network. This implies, quantum instrumentality cannot simulate EPR-nonlocal correlations completely. In contrast, here we show that quantum instrumentality can indeed simulate EPR correlations completely and uniquely if viewed from the perspective of NAQC. Implication of our result is that the entire set of EPR-correlations can be explained by the LHS model in the instrumental causal background if viewed from the perspective of NAQC.
Based on the exact conditional quantum dynamics for a two-ion system, we propose an efficient {\it single-step} scheme for coherently manipulating quantum information of two trapped cold ions by using a pair of synchronous laser pulses. Neither the auxiliary atomic level nor the Lamb-Dicke approximation are needed.
Interaction with a thermal environment decoheres the quantum state of a mechanical oscillator. When the interaction is sufficiently strong, such that more than one thermal phonon is introduced within a period of oscillation, quantum coherent oscillations are prevented. This is generally thought to preclude a wide range of quantum protocols. Here, we introduce a pulsed optomechanical protocol that allows ground state cooling, general linear quantum non-demolition measurements, optomechanical state swaps, and quantum state preparation and tomography without requiring quantum coherent oscillation…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g. concerning the number of computational steps) and it neglects physical systems which cannot follow the "standard circuit model" analysis. We propose a computational scheme which overcomes the notion of the transposition from classical circuits providing a computation scheme with the least possible number of Hamiltonians in order to minimize the physical res…
A diffusion process is usually assumed for the phase of the order parameter of a Bose system of finite size. The theoretical basis is limited to the so called Bogoliubov approximation. We show that a suitable generalization of the Hartree-Fock-Bogoliubov approach recovers phase diffusion.
We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique. Regularization and convolution methods are specifically considered since they are accessible in experiments. We further discuss more general quantum systems for which the concept of negative probabilities can be generalized, being highly relevant for quantum information science. For analyzing quantum superpositions, we apply recently developed approaches to visualize q…
The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multi-time correlation functions, thus requiring full access to the total "system+environment" evolution, and providing a stronger requirement than CP-divisibility. Here, we analyze CP-divisibility and check the validity of quantum regression beyond the Born-Markov approximation (e.g. weak coupling limit) for a class of generalized spin-boson (GSB) models giving rise to a multi-level amplitude-damping evolution; in all cases, it is possible to engineer the system-bath coupling in s…
We propose an optical read-out scheme allowing a demonstration of principle of information extraction below the diffraction limit. This technique, which could lead to improvement in data read-out density onto optical discs, is independent from the wavelength and numerical aperture of the reading apparatus, and involves a multi-pixel array detector. Furthermore, we show how to use non classical light in order to perform bit discrimination beyond the quantum noise limit.
We generalize the experimental success criterion for quantum teleportation/memory in continuous-variable quantum systems to be suitable for non-unit-gain condition by considering attenuation/amplification of the coherent-state amplitude. The new criterion can be used for a non-ideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in quantum domain.
By introducing an operator sum representation for arbitrary linear maps, we develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory of "linear quantum error correction" is applicable in cases where the standard and restrictive assumption of a factorized initial system-bath state does not apply.
It is the purpose of the present contribution to demonstrate that the generalization of the concept of a quantum mechanical observable from the Hermitian operator of standard quantum mechanics to a positive operator-valued measure is not a peripheral issue, allegedly to be understood in terms of a trivial nonideality of practical measurement procedures, but that this generalization touches the very core of quantum mechanics, viz. complementarity and violation of the Bell inequalities.
In this paper we describe that the optically pumped frequency standards can have frequency stability beyond the quantum noise limit by detecting the Ramsey resonance through the squeezed light. In this paper we report that instead of considering the interaction of entangled atoms in the microwave region, it will be more practical to create the entanglement of the atoms in the detection region using the squeezed light, which is also used for the detection of the Ramsey resonance. The advantage of squeezing can be derived when the technical noises have been removed.
Recently, there have been significant developments in entanglement-based quantum metrology. However, entanglement is fragile against experimental imperfections, and quantum sensing to beat the standard quantum limit in scaling has not yet been achieved in realistic systems. Here, we show that it is possible to overcome such restrictions so that one can sense a magnetic field with an accuracy beyond the standard quantum limit even under the effect of decoherence, by using a realistic entangled state that can be easily created even with current technology. Our scheme could pave the way for the r…
The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum objects, for example, a coupled quantum mechanical oscillator to a cavity single photon. In this approach we study the dynamics of such systems in strong coupling regime. We find that, under strong optomechanical coupling, steady quantum states of optomechanical systems driven by continuous-wave single photons exhibit periodic oscillation and cavity noise cons…
We propose a general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be non-classical. Remarkably, we do not assume any classical or quantum formalism to describe the mediating physical system: our result follows from general information-theoretic principles, drawn from the recently proposed constructor theory of information. This argument provides the indispensable theoretical basis for recently proposed tests of non-classicality in gravity, based on witnessing gravitationally-induced entanglement i…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three result…
Acin et al. introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but, in order to account for beyond-quantum correlations, global pseudo-states that are not positive semidefinite are allowed. After a short review of the formalism, we consider its use in the quantification of both general non-local and beyond-quantum correlations. We argue that the unified framework for correlations provides a simple approach to such a quantification, in particular when the quantification is meant to be operational and…
Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level Λ systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure pu…
We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps is implemented with a number of quantum gates which is independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a lattice with $N=4$ point…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision is typically bounded in terms of the variance of an observable.
Recently, the Gaussian optimizer conjecture in quantum information theory was confirmed for bosonic Gaussian gauge-covariant or contravariant channels. These results use the i.i.d. model of the quantum noise. In this paper we consider quantum Gaussian signal+noise model with time-continuous stationary coloured noise. A proof of the coding theorem for the classical capacity of quantum broadband gauge-covariant Gaussian channels is given. We also discuss and compare the "broadband" and the "bandpass" models of time-continuous time-continuous stationary coloured noise.
Spectral homodyne detection, a widely used technique for measuring quantum properties of light beams, cannot retrieve all the information needed to reconstruct the quantum state of spectral field modes. We show that full quantum state reconstruction can be achieved with the alternative measurement technique of resonator detection. We experimentally demonstrate this difference by engineering a quantum state with features that go undetected by homodyne detection but are clearly revealed by resonator detection.
We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the quality of its output does not depend on the input. We also examine a machine which combines a unitary transformation with a selective measurement to produce good copies of states in a neighborhood of a particular state. We discuss the problem of measurement of the output states.
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between Alice and Bob measurements become self correlations between hidden spin values for each particle, together with perfect anti correlation between spin values on the pair. Alice determines through measurement on her particle the value of spin in some direction. Spin in another direction is inferred from Bob measurement on the companion. Bell's inequalities are…
It is nowadays accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a quantum state from entangled to separable and vice versa. We propose to certify the presence of quantumness via an average over all physically relevant modal decompositions. We investigate extremal states for such a measure: SU(2)-coherent states possess the least quantumness whereas the opposite extreme is inhabited by states with maximally spread Majorana constellations.
We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.
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.
Many synthesis approaches for reversible and quantum logic have been proposed so far. However, most of them generate circuits with respect to simple metrics, i.e. gate count or quantum cost. On the other hand, to physically realize reversible and quantum hardware, additional constraints exist. In this paper, we describe cost metrics beyond gate count and quantum cost that should be considered while synthesizing reversible and quantum logic for the respective target technologies. We show that the evaluation of a synthesis approach may differ if additional costs are applied. In addition, a new c…
The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\hbar$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of generalized Lyapunov exponents, with these results applying in the near-classical regime. We present results for a specific system going well beyond earlier work, considering how these dynamics are altered for the Duffing problem by changing $\hbar,D$ and show that the entropy dynamics have a transition from classical to quantum behavior that scales, at least for…
A scheme to implement quantum logic gates by manipulating trapped ions through interaction with monochromatic external laser field and quantized cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times, for implementing ionic state transitions using non-resont laser pulse or quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter value of $η_{L}=η_{c}=0.2$, and is seen to decrease further with increase in number of initial state vibrational quanta $m$.
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples.
