Superposition, Entanglement and Other Oddities

In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting “time-symmetrized” interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics.

The quantum mechanical measurement process is analysed in detail, especially from the group theoretical point of view. The first three chapters review the results obtained before briefly. In §1, the classical theory of measurement, originated by von Neumann, is birefly described. The importance of considering more general schemes of measurements than the original one is, however, emphasized In §2, the role of conservation laws, in imposing limitations on the possibility of measurements, is discussed. Accurately measurable quantities are defined in this context. In §3, the role of conservation laws is further analysed. It is shown that the conserved quantity of the apparatus cannot be used for a “pointer reading.” The following two chapters discuss the nature of the exactly measurable quantities. In §4, exactly measurable quantities are explicitly determined. It is shown that the measurement of projection operators in the Hilbert space of the object which commute with the operators of the restricted Poincare group give all the information on the states of the object that can be obtained by accurate measurements. In §5, the measurement on objects which are composed of more than one particle is discussed.

This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.

The effect of filtering operation with respect to purification and concentration of entanglement in quantum states are discussed in this paper. It is shown, through examples, that the local action of the filtering operator on a part of the composite quantum state allows for purification of the remaining part of the state. The redistribution of entanglement in the subsystems of a noise affected state is shown to be due to the action of local filtering on the non-decohering part of the system. The varying effects of the filtering parameter, on the entanglement transfer between the subsystems, depending on the choice of the initial quantum state is illustrated.

The dynamics of the coherent superposition of exciton states in a semiconductor quantum well excited by the joint action of two successive light pulses with the time interval between them t12 has been theoretically studied. The dependences of the amplitude and initial phase of the quantum bits on t12 have been found. It has been shown that the time dependence of the Kerr rotation of the reflected probe pulse is determined not only by the dynamics of the excited state, but also by the optical properties of the heterostructure containing the quantum well. The dependence of the decay rate of the excited state on t12 has been predicted.

Photon's dual nature, manifesting as both wave-like and particle-like behavior, is a phenomenon known as wave-particle duality and remains one of the most perplexing mysteries in quantum mechanics. In this work, we explore the relationships among the wave behavior, particle behavior, and entanglement of quantum states. We show the strong complementary relationships for bipartite isolated systems in terms of the generalized quantum entropic measures. This provides a measure-independent result going beyond all the existing complementary results based on specific measures. We further extend the results for non-isolated systems.

Hughston has recently proposed a stochastic extension of the Schrödinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston’s equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston’s equation to earlier work on norm-preserving stochastic equations, and show that Hughston’s equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston’s, suffices to give an objective interpretation of the measurement process in quantum mechanics.

Emotional sentience and the nature of phenomenal experience

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.

Multiparticle entanglement enables quantum simulations, quantum computing, and quantum-enhanced metrology. Yet, there are few methods to produce and measure such entanglement while maintaining single-qubit resolution as the number of qubits is scaled up. Using atom chips and fiber-optical cavities, we have developed a method based on nondestructive collective measurement and conditional evolution to create symmetric entangled states and perform their tomography. We demonstrate creation and analysis of entangled states with mean atom numbers up to 41 and experimentally prove multiparticle entanglement. Our method is independent of atom number and should allow generalization to other entangled states and other physical implementations, including circuit quantum electrodynamics.

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theorry of axion field arising from Type IIB string theory compactified to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For massless axion field, in all these three formalism, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

Bipolar quantum agent (BQA), bipolar quantum geometry (BQG) and bipolar dynamic logic (BDL) are introduced based on bipolar complementarity – a logical extension to Niels Bohr’s particle-wave YinYang duality principle. Complete geometrical background independence is proposed and BQG is proven completely background independent which leads to the notion of bipolar quantum superposition – an equilibrium-based logical approach to superposition. It is shown that the logical linearity of BDL can be unified with the physical nonlinearity of bipolar dynamic equilibrium. It is proven that a single polarized photon as a BQA can be logically channeled through the three polarizers in Dirac’s experiment with BDL regardless of quantum uncertainty. It is illustrated that BQG, BDL and bipolar probability adds analytical power to quantum mechanics. It is concluded that bipolar quantum superposition demystifies Schrodinger’s cat paradox from a weird quantum phenomenon to a logically comprehendible YinYang bipolar dynamic equilibrium interpretation of quantum superposition and leads to an analytical paradigm of quantum mechanics and quantum biology as presented in Part II of this work.

Time fractional evolution of a single quantum state and entangled state

Deterministic sources of high-fidelity entangled qubit pairs encoded in the dual-rail photonic basis, i.e., presence of a single photon in one of two orthogonal modes, are a key enabling technology of many applications of quantum information processing, including high-rate, high-fidelity quantum communications over long distances. The most popular and mature sources of such photonic entanglement, e.g., those that leverage spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, generate an entangled (so-called continuous-variable) quantum state that contains contributions from high-order photon terms that lie outside the span of the dual-rail basis, which is detrimental to most applications. One often uses low pump power to mitigate the effects of those high-order terms. However, that reduces the pair generation rate, and the source becomes inherently probabilistic. We investigate a cascaded source that performs a linear-optical entanglement swap between two SPDC sources, to generate a heralded photonic entangled state that has a higher fidelity (to the ideal Bell state) compared to a free-running SPDC source. Furthermore, with the Bell swap providing a heralding trigger, we show how to build a multiplexed source, which despite reasonable switching losses and detector loss and noise, yields a fidelity versus success probability trade-off of a high-efficiency source of high-fidelity dual-rail photonic entanglement. We find, however, that there is a threshold of $1.5$ dB of loss per switch, beyond which multiplexing hurts the fidelity versus success probability trade-off.