Uniting Precision Measurement and Quantum Control

Phase control of a single-frequency continuous-wave laser and the electric field of a mode-locked femtosecond laser has now reached the same level of precision, resulting in sub-optical-cycle phase coherence being preserved over macroscopic observation times exceeding seconds. The subsequent merge of CW laser-based precision optical- frequency metrology and ultra-wide-bandwidth optical frequency combs has produced remarkable and unexpected progress in precision measurement and ultrafast science. A phase-stabilized optical frequency comb spanning an entire optical octave （ 〉 300 THz） establishes millions of marks on an optical frequency ＂ruler＂ that are stable and accurate at the Hz level. Accurate phase connections among different parts of electromagnetic spectrum, including optical to radio frequency, are implemented. These capabilities have profoundly changed＇ the optical frequency metrology, resulting in recent demonstrations of absolute optical frequency measurement, optical atomic clocks, and optical frequency synthesis. Combined with the use of ultracold atoms, optical spectroscopy and frequency metrology at the highest level of precision and resolution are being accomplished at this time. The parallel developments in the time domain applications have been equally revolutionary, with precise control of the pulse repetition rate and the carrier-envelope phase offset both reaching the sub-femtosecond regime. These developments have led to recent demonstrations of coherent synthesis of optical pulses from independent lasers, coherent control in nonlinear spectroscopy, coherent pulse addition without any optical gain, and coherent generation of frequency combs in the VUV and XUV spectral regions. Indeed, we now have the ability to perform completely arbitrary, optical, waveform synthesis, complement and rival the similar technologies developed in the radio frequency domain. With this unified approach on time and frequency domain controls,     

Quantum Mechanics: An Intelligible Description of Objective Reality?

Jim Cushing emphasized that physical theory should tell us an intelligible and objective story about the world, and concluded that the Bohm theory is to be preferred over the Copenhagen interpretation. We argue here, however, that the Bohm theory is only one member of a wider class of interpretations that can be said to fulfill Cushings desiderata. We discuss how the pictures provided by these interpretations differ from the classical one. In particular, it seems that a rather drastic form of perspectivalism is needed if accordance with special relativity is to be achieved.     

Quantum Generalized Subspace Projector Measurement and Measurement Induced Entanglement

We propose the concept of the quantum generalized subspace projector measurement （QGSPM）. The distinguished properties of QGSPM is revealed： no matter what the state of the system is prior to the measurement and what the measured result occurs, the state posterior to the measurement can be collapsed onto the specified subspace. Subsequently, the quantum generalized case-projector measurement （QGCPM）, as a special case of QGSPM, is also discussed carefully. It is demonstrated that no matter what measured result occurs, the state of the system posterior to QGCPM can be collapsed into one of pure states. Consequently, QGCPM can be used to generate the maximally entangled pure states for multiple particles. As illustrative examples, several concrete methods of generating entanglement are proposed for two two-level particles. It is found that the maximally entangled pure states of two 2-level particles can be generated just by a single QGCPM and the corresponding QGCPM operators are physically realizable in principle if an ancillary four-dimensional quantum system can be introduced.     

Entanglement and Quantity in Quantum Space-- About Quantum Measurement (Ⅱ)

As a continuation and extension of "quantity in phase space" "quantity in quantum space" is introduced. With that, the disappearing of quantum interference discussed in a previous paper [S. Dürr, et al., Nature 395 (1998) 33] is explained in the same spirit as our recent papers [Ren De-Ming, Commun. Theor. Phys. (Beijing, China) 41 (2004) 685, 833].     

A Representation of Quantum Measurement in Order-Unit Spaces

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.     

A Representation of Quantum Measurement in Nonassociative Algebras

Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the search for such examples of the structure mentioned above that do not stem from Jordan operator algebras; first natural candidates are matrix algebras over the octonions and other nonassociative rings. Therefore, the case when a nonassociative commutative multiplication exists is studied without assuming that it satisfies the Jordan condition. The characteristics of the resulting algebra are analyzed. This includes the uniqueness of the spectral resolution as well as a criterion for its existence, subalgebras that are Jordan algebras, associative subalgebras, and more different levels of compatibility than occurring in standard quantum mechanics. However, the paper cannot provide the desired example, but contribute to the search by the identification of some typical differences between the potential examples and the Jordan operator algebras and by negative results concerning some first natural candidates. The possibility that no such example exists cannot be ruled out. However, this would result in an unexpected new characterization of Jordan operator algebras, which would have a significant impact on quantum axiomatics since some customary axioms (e.g., power-associativity or the sum postulate for observables) might turn out to be redundant then.     

Entanglement and Quantity in Quantum Space —— About Quantum Measurement （II）

As a continuation and extension of “quantity in phase space“ “quantity in quantum space“ is introduced. With that, the disappearing of quantum interference discussed in a previous paper [S. Du^err, et al., Nature 395 (1998) 33] is explained in the same spirit as our recent papers [Ren De-Ming, Commun. Theor. Phys. (Beijing, China) 41(2004) 685, 833].     

Quantum Locality,Rings a Bell?: Bell’s Inequality Meets Local Reality and True Determinism

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics (QM) based on the notion of ontological states proposed by ’t Hooft (The cellular automaton interpretation of quantum mechanics, arXiv:1405.1548v3, 2015; Springer Open 185,  https://doi.org/10.1007/978-3-319-41285-6, 2016). We view these ontological states as the ones embedded with realism and compare them to the (usual) quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell’s inequality: the usual inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way.     

Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality

The quantum discrete Liouville model in the strongly coupled regime, 1 < c < 25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by Hermitian conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables. Received: 26 May 2000 / Accepted: 28 May 2000     

A New Approach of Quantum Mechanics for Neutron Single-Slit Diffraction

Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments are explained by many theoretical works. We study neutron single-slit diffraction with a quantum mechanical approach. It is found that the obvious diffraction patterns can be obtained when the single- slit width a is in the range of 3λ - 60λ. We also lind a new quantum effect of the thickness of single-slit which can make a large impact on the diffraction pattern. The new quantum effect predicted in our work can be tested by the neutron single-slit diffraction experiment.     

Zero-Point Vacancy Concentration in a Model Quantum Solid: A Reversible-Work Approach

We investigate the influence of anharmonic effects on the zero-point vacancy concentration in a boson system model in the solid phase at T=0 K. We apply the reversible-work method to compute the vacancy formation free energy and the vacancy concentration in the system. A comparison of our results with those obtained using the harmonic approximation show that anharmonic effects reduce the formation free energy by ∼25%, leading to an increase of the zero-point vacancy concentration by more than an order of magnitude.     

\mathcal{A} -invariance: An Axiomatic Approach to Quantum Relativity

The sort of approach claimed by the title of this article is realizable, at least, within the framework of ADG where we do not assume any “spacetime” supplying the dynamics we employ. The latter classical type of argument can naturally be included herewith along with its concomitant impediments that are emanated therefrom and are essentially “absorbed”, technically speaking, by the proposed mechanism. So our approach, being “manifoldless” (thence, no smoothness, in the standard sense) does not contain any such issue, as before, according to the very definitions, being thus “singularities”-free. As a consequence, the equations that one would be able to formulate within the present set-up will be, by the very essence of the matter, already the quantized ones. Dedicated to Professor Rafael D. Sorkin on the occasion of his 60th birthday with much friendship and recognition of his creative pursuit in theoretical physics.     

A Strengthened Monotonicity Inequality of Quantum Relative Entropy: A Unifying Approach Via Rényi Relative Entropy

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of \({\alpha}\)-Rényi relative entropy. We develop a unifying treatment toward the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extend some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest.     

A Classical Formulation of Quantum Theory?

We explore a particular way of reformulating quantum theory in classical terms, starting with phase space rather than Hilbert space, and with actual probability distributions rather than quasiprobabilities. The classical picture we start with is epistemically restricted, in the spirit of a model introduced by Spekkens. We obtain quantum theory only by combining a collection of restricted classical pictures. Our main challenge in this paper is to find a simple way of characterizing the allowed sets of classical pictures. We present one promising approach to this problem and show how it works out for the case of a single qubit.     

A Geometric Approach to Time Evolution Operators of Lie Quantum Systems

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrödinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.     

Quantum Dynamics with Mean Field Interactions: a New Approach

We propose a new approach for the study of the time evolution of a factorized N-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new technique, which is based on the control of the growth of the correlations among the particles, leads to quantitative bounds on the difference between the many-particle Schrödinger dynamics and the one-particle nonlinear Hartree dynamics. In particular the one-particle density matrix associated with the solution to the N-particle Schrödinger equation is shown to converge to the projection onto the one-dimensional subspace spanned by the solution to the Hartree equation with a speed of convergence of order 1/N for all fixed times.     

Quantum Teleportation and Quantum Information Splitting by?Using?a?Genuinely?Entangled Six-Qubit State

A new application of the genuinely entangled six-qubit state introduced recently by Tapiador et al. (J. Phys. A 42:415301, 2009) is investigated for the quantum teleportation of an arbitrary three-qubit state and for quantum information splitting (QIS) of an arbitrary two-qubit state. For QIS, we have shown that it can be completed perfectly with two distinct measurement methods. In our scheme, the joint Bell-state measurement and the joint multi-qubit measurement are needed. This quantum teleportation and QIS schemes are deterministic.