Abstract: The problem of ”what is ’system’? ” is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of mutually non-interacting, non-entangled systems to employ entanglement of the newly defined ”(sub)systems ” consisting the one and the same composite system. Given the different divisions of a composite system into ”subsystems”, the Hamiltonian of the system may generate in general non-equivalent quantum computations. Redefinition of ”subsystems” of a composite system may be regarded as a method for avoiding decoherence in the quantum hardware. In principle, all the notions refer to a composite system as simple as the hydrogen atom. 1.
Abstract: The problem of ”what is ’system’? ” is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of mutually non-interacting, non-entangled systems to employ entanglement of the newly defined ”(sub)systems ” consisting the one and the same composite system. Given the different divisions of a composite system into ”subsystems”, the Hamiltonian of the system may generate in general non-equivalent quantum computations. Redefinition of ”subsystems” of a composite system may be regarded as a method for avoiding decoherence in the quantum hardware. In principle, all the notions refer to a composite system as simple as the hydrogen atom. 1.
Introduction We will now turn to quantum entanglements and their contemporary, possibly practical, interest. Entanglements, first discussed in the E.P.R. paradox (Einstein, Podolsky, Rosen, 1935) are a perplexing nonlocal feature of quantum mechanics. This was immediately and succinctly discussed by Schrödinger (1935). The long history of this apparent paradox is outlined in the wonderful book of Jammer (1974). We will not focus on the central issue of “hidden variables” and their resolution by the Bell inequalities (Bell, 1964) and the test, nor the failure, of these in experiment (see Fry, 1998). The distinctive quantum nature of entanglements has led to two quantum effects which we will discuss: quantum information teleportation (Zeilenger, 1998) and quantum computation by means of entangled states. A nice, recent, elementary introduction to the latter is in the Los Alamos reports of James and Kwiat (2002). The quantum correlations or entanglements are sensitive to environmental destruction. This was pointed out early by Zurek, who termed this “decoherence.” The loss of coherence may occur on a short time scale. Recent discussions have been given by Zurek (2002, 2003). We have already given a theoretical example early in Chapter 2. It is pertinent to discuss this here, since it is a property of opensystem quantum master equations that is a central part of our study in this book. In a sense, the decoherence of correlations has turned out to be a “practical” application of these theoretical notions. Are there remedies for unwanted decoherence? Quantum error correction is a possibility. This will be mentioned also. Entanglements: foundations Following the reading of the E.P.R. paper, Schrödinger (1935b) quickly repeated the argument from quantum theory, but more generally. He introduced the term “entanglement” to describe what he seemed to agree was a curious, if not unacceptable, property. Let us follow his point of view. Given a state ψ ( x, y ) of a composite system of particles x and y formed in their mutual interaction. ψ ( x , y ) is not a product state.
Reference frames are of special importance in physics. They are usually considered to be idealized entities. However, in most situations, e.g. in laboratories, physical processes are described within reference frames constituted by physical systems. As new technological developments make it possible to demonstrate quantum properties of complex objects an interesting conceptual problem arises: Could one use states of quantum systems to define reference frames? Recently such a framework has been introduced in [F. Giacomini, E. Castro-Ruiz, and Č. Brukner, Nat Commun 10, 494 (2019)]. One of its consequences is the fact that quantum correlations depend on a physical state of an observers reference frame. The aim of this work is to examine the dynamical aspect of this phenomena and show that the same is true for correlations established during an evolution of a composite systems. Therefore, decoherence process is also relative: For some observers the reduced evolution of subsystems is unitary, whereas for others not. I also discuss implications of this results for modern developments of decoherence theory: Quantum Darwinism and Spectrum Broadcast Structures.
Composition of Different and of Identical Systems It is a general tendency of physics to interpret physical systems as composed of simpler, more elementary subsystems. The question “What is it made of?” is a very tempting and popular one. Though this attitude does not reflect a logical necessity, it has proved to be successful in significant circumstances: we think, e.g., of macroscopic matter as composed of atoms and molecules, of molecules as composed of atoms, of atoms as composed of nuclei and electrons, and of nuclei as composed of protons and neutrons. Loosely speaking, one might expect that this attitude will be successful whenever the interaction that packs the constituent subsystems together is not strong enough to make them lose their identity. Here, we are concerned with the problem of constructing the quantum-mechanical formalism of a compound system knowing the formalisms of the constituent subsystems. Thus our first problem is to specify the Hilbert space of the compound system. For the sake of simplicity, let us restrict ourselves to the case of a system composed of only two subsystems. The prescriptions of quantum theory vary according to whether one is faced with the composition of identical or nonidentical subsystems.
Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck–Einstein relation between energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex.
Abstract Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In particular we will focus our attention to composite quantum systems composed of identical constituents, with the purpose of dealing with subtle issues, which have never been adequately discussed in the literature, originating from the true indistinguishability of the subsystems involved.
Understanding a composite system through its constituents is a fundamental practice in physics. In the context of quantum reference frames (QRFs), however, combining the usual quantum-theoretic notion of composition with QRF perspectives gives rise to subtle issues, such as the 'paradox of the third particle'. Here we study in depth how to compose subsystems in QRF perspectives, building on a recent formalism for QRFs [E.Castro-Ruiz and O.Oreshkov, 2025]. We first show how the frames of external observers can be internalised and treated within the framework. This establishes a consistent hierarchy of QRF perspectives, which we use to define the adding and removing of subsystems. We then explain how, owing to the so-called 'extra-particle' degrees of freedom, the formalism gives a consistent treatment of subsystems, avoiding any paradoxes by construction. Consistency then implies that composing subsystems in a QRF perspective differs from, and generalises, the standard quantum-theoretic case. In particular, not every state can be appended in tensor-product form relative to a QRF, and we characterise the set of compatible states. Finally, we introduce 'classicalisation', a procedure that recovers a classical-like perspective from a general QRF. This procedure circumvents the aforementioned state restrictions but carries a different operational meaning, which we study through a concrete example.