The Quantum World is not Built up from Correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The Bell inequality argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.     

Superstrings and the Foundations of Quantum Mechanics

It is put forward that modern elementary particle physics cannot be completely unified with the laws of gravity and general relativity without addressing the question of the ontological interpretation of quantum mechanics itself. The position of superstring theory in this general question is emphasized: superstrings may well form exactly the right mathematical system that can explain how quantum mechanics can be linked to a deterministic picture of our world. Deterministic interpretations of quantum mechanics are usually categorically rejected, because of Bell’s powerful observations, and indeed these apply here also, but we do emphasize that the models we arrive at are super-deterministic, which is exactly the case where Bell expressed his doubts. Strong correlations at space-like separations could explain the apparent contradictions.     

Local Information as an Essential Factor for Quantum Entanglement

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.     

Limit on nonlocality in any world in which communication complexity is not trivial

Bell proved that quantum entanglement enables two spacelike separated parties to exhibit classically impossible correlations. Even though these correlations are stronger than anything classically achievable, they cannot be harnessed to make instantaneous (faster than light) communication possible. Yet, Popescu and Rohrlich have shown that even stronger correlations can be defined, under which instantaneous communication remains impossible. This raises the question: Why are the correlations achievable by quantum mechanics not maximal among those that preserve causality? We give a partial answer to this question by showing that slightly stronger correlations would result in a world in which communication complexity becomes trivial.     

On probability theory and probabilistic physics—Axiomatics and methodology

A new formulation involving fulfillment of all the Kolmogorov axioms is suggested for acomplete probability theory. This proves to be not a purely mathematical discipline. Probability theory deals with abstract objects—images of various classes of concrete objects—whereas experimental statistics deals with concrete objects alone. Both have to be taken into account. Quantum physics and classical statistical physics prove to be different aspects ofone probabilistic physics. The connection of quantum mechanics with classical statistical mechanics is examined and the origin of the Schrödinger equation is elucidated. Attention is given to the true meaning of the wave-corpuscle duality, and the incompleteness of nonrelativistic quantum mechanics is explained.     

A probabilistic approach to quantum mechanics based on ‘tomograms’

It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical‐like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed.     

Quantum state transfer between light and matter via teleportation

Quantum teleportation is an interesting feature of quantum mechanics. Entanglement is used as a link between two remote locations to transfer a quantum state without physically sending it – a process that cannot be realized utilizing merely classical tools. Furthermore it has become evident that teleportation is also an important element of future quantum networks and it can be an ingredient for quantum computation. This article reports for the first time the teleportation from light to atoms. In the experiment discussed, the quantum state of a light beam is transferred to an atomic ensemble. The key element of light‐atom entanglement created via a dispersive interaction lays the foundation for the protocol.     

Work and work fluctuations in quantum systems

With the development of quantum thermodynamics [1], it turned out that the existence of a thermal equilibrium can be derived directly from quantum mechanics. This finding has raised the question, what other thermodynamic concepts could be applied to quantum systems and how they might emerge from quantum mechanics. Here, we discuss how the concept of work translates to quantum systems and how its emergence can be understood. Moreover, we show that even for small and simple quantum systems, work may be a meaningful concept. We then address the question of work fluctuations in quantum systems. We discuss the Jarzynski relation and its quantum counterparts and we show that corresponding relations hold even for open quantum systems.     

Objective Probability and Quantum Fuzziness

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation.     

On the unique mapping relationship between initial and final quantum states

In its standard formulation, quantum mechanics presents a very serious inconvenience: given a quantum system, there is no possibility at all to unambiguously (causally) connect a particular feature of its final state with some specific section of its initial state. This constitutes a practical limitation, for example, in numerical analyses of quantum systems, which often make necessary the use of some extra assistance from classical methodologies. Here it is shown how the Bohmian formulation of quantum mechanics removes the ambiguity of quantum mechanics, providing a consistent and clear answer to such a question without abandoning the quantum framework. More specifically, this formulation allows to define probability tubes, along which the enclosed probability keeps constant in time all the way through as the system evolves in configuration space. These tubes have the interesting property that once their boundary is defined at a given time, they are uniquely defined at any time. As a consequence, it is possible to determine final restricted (or partial) probabilities directly from localized sets of (Bohmian) initial conditions on the system initial state. Here, these facts are illustrated by means of two simple yet physically insightful numerical examples: tunneling transmission and grating diffraction.     

基于量子隐形传态的量子保密通信方案

量子保密通信包括量子密钥分发、量子安全直接通信和量子秘密共享等主要形式.在量子密钥分发和秘密共享中,传输的是随机数而不是信息,要再经过一次经典通信才能完成信息的传输.在量子信道直接传输信息的量子通信形式是量子安全直接通信.基于量子隐形传态的量子通信(简称量子隐形传态通信)是否属于量子安全直接通信尚需解释.构造了一个量子隐形传态通信方案,给出了具体的操作步骤.与一般的量子隐形传态不同,量子隐形传态通信所传输的量子态是计算基矢态,大大简化了贝尔基测量和单粒子操作.分析结果表明,量子隐形传态通信等价于包含了全用型量子密钥分发和经典通信的复合过程,不是量子安全直接通信,其传输受到中间介质和距离的影响,所以不比量子密钥分发更有优势.将该方案与量子密钥分发、量子安全直接通信和经典一次性便笺密码方案进行对比,通过几个通信参数的比较给出各个方案的特点,还特别讨论了各方案在空间量子通信方面的特点.     

Proposed experiment to test the bounds of quantum correlations

The combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt inequality can give values between the classical bound, 2, and Tsirelson's bound, 2 x square root of 2. However, for a given set of local observables, there are values in this range which no quantum state can attain. We provide the analytical expression for the corresponding bound for a parametrization of the local observables introduced by Filipp and Svozil, and describe how to experimentally trace it using a source of singlet states. Such an experiment will be useful to identify the origin of the experimental errors in Bell's inequality-type experiments and could be modified to detect hypothetical correlations beyond those predicted by quantum mechanics.     

Correlation and Information in Quantum Channels

Quantum and classical correlations in quantum channels are investigated by means of an entangled pure state and a separable state which is closest to an entangled pure state. The coherent information and the separable information are used to estimate how much correlation is transmitted through a quantum channel. As the examples, the linear dissipative channel of qubits and the quantum erasure channel are considered.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?

The interpretation of the concept of reduced state is a subtle issue that has relevant consequences when the task is the interpretation of quantum mechanics itself. The aim of this paper is to argue that reduced states are not the quantum states of subsystems in the same sense as quantum states are states of the whole composite system. After clearly stating the problem, our argument is developed in three stages. First, we consider the phenomenon of environment-induced decoherence as an example of the case in which the subsystems interact with each other; we show that decoherence does not solve the measurement problem precisely because the reduced state of the measuring apparatus is not its quantum state. Second, the non-interacting case is illustrated in the context of no-collapse interpretations, in which we show that certain well-known experimental results cannot be accounted for due to the fact that the reduced states of the measured system and the measuring apparatus are conceived as their quantum states. Finally, we prove that reduced states are a kind of coarse-grained states, and for this reason they cancel the correlations of the subsystem with other subsystems with which it interacts or is entangled.     

Proposal to Test a Transient Deviation from Quantum Mechanics’ Predictions for Bell’s Experiment

Quantum mechanics predicts correlations between measurements performed in distant regions of a spatially spread entangled state to be higher than allowed by intuitive concepts of Locality and Realism. These high correlations forbid the use of nonlinear operators of evolution (which would be desirable for several reasons), for they may allow faster-than-light signaling. As a way out of this situation, it has been hypothesized that the high quantum correlations develop only after a time longer than L/c has elapsed (where L is the spread of the entangled state and c is the velocity of light). In shorter times, correlations compatible with Locality and Realism would be observed instead. A simple hidden variables model following this hypothesis is described. It is based on a modified Wheeler–Feynman theory of radiation. This hypothesis has not been disproved by any of the experiments performed to date. A test achievable with accessible means is proposed and described. It involves a pulsed source of entangled states and stroboscopic record of particle detection during the pulses. Data recorded in similar but incomplete optical experiments are analyzed, and found consistent with the proposed model. However, it is not claimed, in any sense, that the hypothesis has been validated. On the contrary, it is stressed that a complete, specific test is absolutely needed.     

Quantum States as Objective Informational Bridges

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.