Narrow Results

We provide a justification, via the thermodynamic limit, of the modular formula for entropy production in two-time measurement proposed in [T. Benoist, L. Bruneau, V. Jakšić, A. Panati and C.-A. Pillet, A note on two-times measurement entropy production and modular theory, Lett. Math. Phys.114:32 (2023), doi:10.1007/s11005-024-01777-0]. We consider the cases of open quantum systems in which all thermal reservoirs are either (discrete) quantum spin systems or free Fermi gases.

Feynman proposed a postulate or a method of quantization in his celebrated paper in 1948. Applying Feynman’s postulate to temporally continuous quantum measurements of the positions of particles, Mensky proposed the restricted Feynman path integrals (RFPIs) for continuous quantum measurements after phenomenological considerations. Our aim in this paper is to give a rigorous proof that Mensky’s RFPIs emerge out of Feynman’s postulate under a simple approximation. In addition, it is proved that the RFPIs emerge out of von Neumann’s postulate on instantaneous measurements as well as Feynman’s postulate. The quantum systems that we study include spin systems. These results are applied to formulations of the multi-split experiments, the quantum Zeno and the Aharonov–Bohm effects.

Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the performance of experimental quantum gates, it is therefore necessary to identify the essential features that indicate quantum coherent operation. In this paper, we show that an efficient characterization of an experimental device can be obtained by investigating the classical logic operations on a pair of complementary basis sets. It is then possible to obtain reliable predictions about the quantum coherent operations of the gate such as entanglement generation and Bell state discrimination even without performing these operations directly.

The framework of the generalized theory of quantum measurement provides some theoretical tools for computing flavor associated energies correlated to the von-Neumann entropy of a composed system. After defining flavor-averaged and flavor-weighted energies, that are respectively supported by nonselective (selective) quantum measurement schemes, the right correlation between the energies of flavor eigenstates and their measurement probabilities can be obtained. Our results from the composed quantum system framework show that the nonselective measurement scheme for computing flavor-weighted energies is consistent with predictions from single-particle quantum mechanics. As an application of our results, through the expressions for neutrino effective mass values, it is straightforwardly verified that cosmological background neutrino energy densities could be obtained from the coherent superposition of mass eigenstates.

Reiterated or continuous measurement on a quantum system impedes the quantum object's evolution. This "quantum Zeno" effect (QZE), contemplated for decades, has been conventionally attributed to the reaction of the measuring device on the quantum object being measured, in the sense of the Heisenberg microscope. However, even reactionless "quantum non-demolition" measurements seem to qualify for that inhibition to take place and may constitute a "quantum Zeno paradox" (QZP). An experimental proof of QZE had been attempted in the past on clouds of ions confined in a Paul trap. In the meantime it has been shown, however, that the anticipated impediment of the quantum evolution by a sheer gain of information, i.e. by reactionless measurement cannot be, in principle, proven with an ensemble. Recently, experiments have been performed with the use of a single quantum system: an ¹⁷²Yb⁺ ion, laser-driven on its E2 line S_1/2 - D_5/2, or an ¹⁷¹Yb⁺ ion, microwave-driven on its ground-state hyperfine resonance. The results of these experiments demonstrate that mere gain of information on the quantum system, while lacking dynamic action, modifies the system's evolution as it is predicted by quantum mechanics, based on the system's preparation. This seems plausible if we attribute reality to the results of the measurements. If, in contrast, reality is claimed for the prediction, two-fold discontinuity must be admitted: loss of coherence with potential measurements, and renormalization from the results of actual measurements.

Quantum control strategy is discussed from the perspective of quantum information. First, the constraints imposed on quantum control by quantum theory are analyzed. Then some quantum control schemes based on quantum information are discussed, such as teleportation-based distant quantum control, quantum feedback control using quantum cloning and state recognition, quantum control based on measurement and Grover iteration. Finally, some applications of quantum control theory in quantum information and quantum computation such as quantum error correction coding, universality analysis of quantum computation, feedback-induced entanglement enhancement, etc., are presented and the potential applications of quantum control are also prospected.

In this paper, we discuss a proposal for the transfer of states belonging to the W-type states by executing a controlled teleportation protocol. A 7-qubit quantum entangled resource shared between the sender, receiver and controller is utilized in this protocol. The scheme proposed here is a perfect communication scheme where the task of quantum state transfer is performed with certainty. Further, a protocol for the generation of the quantum resource used here is designed and run on IBM platform. Additionally, we consider the effect of four types of noises, namely, amplitude-damping noise, bit-flip noise, phase-flip noise and phase-damping noise on our protocol. The efficiency of the protocol is compared with other similar protocols which shows that the present one is better performing.

There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace dynamics is an underlying classical dynamics of noncommuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature — a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from trace dynamics to show that classical time is a thermodynamic approximation to an operator time in quantum gravitational physics. This prediction will be put to test by ongoing laboratory experiments attempting to construct superposed states of macroscopic objects.

Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity (QGR), because the allowed quantum states must obey the Hamiltonian constraint. (ii) During a quantum measurement, the state of the quantum system randomly collapses from being in a linear superposition of the eigenstates of the measured observable, to just one of the eigenstates, in apparent violation of the predictions of the deterministic, linear Schrödinger equation. (iii) The observed value of the cosmological constant is exceedingly small, compared to its natural value, creating a serious fine-tuning problem. In this essay, we propose a novel idea to show how the three problems help solve each other.

In 2002, Krishna and Parthasarathy⁷ derived discrete quantum version of Maassen–Uffink⁸ entropic uncertainty principle. In this paper, using the notion of continuous operator-valued frames, we derive an entropic uncertainty principle for arbitrary family of operators indexed by measure spaces having finite measure. We give an application to the special case of compact groups.

Quantum teleportation is one of the most important manifestations of nonlocal nature. The basic theory and experiment are explained and reviewed for a qubit system and a continuous-variable system.

A thought experiment, proposed by Karl Popper, which has been experimentally realized recently, is critically examined. A basic flaw in Popper's argument which has also been prevailing in subsequent debates, is pointed out. It is shown that Popper's experiment can be understood easily within the Copenhagen interpretation of quantum mechanics. An alternate experiment, based on discrete variables, is proposed, which constitutes Popper's test in a clearer way. It refutes the argument of absence of nonlocality in quantum mechanics.

We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is that, in this logical framework, symmetry and paraconsistency hold.

The debate about the non-locality of quantum mechanics is old, but still lively. Numerous people use non-locality as (bad) shorthand for quantum entanglement. But some have a long-standing commitment to the validity of this characterization. This paper examines two separate streams in this debate. The first is the arguments of Stapp, and especially his recent paper where he simplifies his contractual argument in the Hardy situation to argue for the non-locality of quantum mechanics. He has maintained his contention that an analysis of a Hardy-type correlation between two spatially separated observers proves that quantum mechanics itself is non-local, without any additional assumption of realism or hidden variables. In the second section, I try to carefully examine the Bell argument in the CHSH variant to see where the difference between the quantum and classical situations differ.

Asher Peres was one of the great physicists of the late 20th century, especially for his intense concern with the fundamental nature of quantum mechanics. His courage in devoting his life to an area many considered "philosophical" (i.e. non-physical) paved the way for the rest of us to reveal our interests and confusions about this area. I am not sure that he would agree with everything in this paper, but I offer it as a tribute to him.

We consider a class of entangled states of a quantum system (S) and a second system (A) where pure states of the former are correlated with mixed states of the latter, and work out the entanglement measure with reference to the nearest separable state. Such "pure-mixed" entanglement is expected when the system S interacts with a macroscopic measuring apparatus in a quantum measurement, where the quantum correlation is destroyed in the process of environment-induced decoherence whereafter only the classical correlation between S and A remains, the latter being large compared to the former. We present numerical evidence that the entangled S–A state drifts towards the nearest separable state through decoherence, with an additional tendency of equimixing among relevant groups of apparatus states.

A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.

Measurement of a degenerate (or non-degenerate) discrete observable is investigated in the framework of quantum measurement theory short of collapse, i.e. premeasurement theory, based on a unitary evolution operator that includes the measurement interaction between object and measuring instrument. A pointer observable with eigen-projectors of, in general, many (or even infinitely) dimensional ranges is introduced as a new approach. It leads to redundant entanglement in the final state. As the first main result, the basic dynamical relation of the approach is derived. It is shown to be equivalent to the calibration condition, which is known to define general exact measurement. The latter is given a practical form. Complete measurement (premeasurement with objectification or collapse), which is in some sense implied by the premeasurement theory, performed on a subsystem of a bipartite object in a pure state is studied with particular attention to its effect on the opposite, interactionally unaffected subsystem. The change of state of the latter is derived for exact complete subsystem measurement, and it is shown that the change is the same as for the simplest, i.e. ideal measurement (this is the second main result). It is applied to the case of twin observables and thus distant measurement obtains a new, more satisfactory, foundation (the third main result). Distant measurement is a basic concept in the EPR phenomenon. The well-known importance of the latter implies importance of the former.

A simple quantum interaction is analyzed, where the paths of two superposed particles asymmetrically cross, while a detector set to detect an interaction between them remains silent. Despite this negative result, the particles' states leave no doubt that a peculiar interaction has occurred: One particle's momentum is changed while the other's remains unaffected, in apparent violation of momentum conservation. Revisiting the foundations of the standard quantum measurement process offers the resolution. Prior to the macroscopic recording of no interaction, a brief critical interval (CI) prevails, during which the particles and the detector's pointer form a subtle entanglement which immediately dissolves. It is this self-cancellation, henceforth "quantum oblivion (QO)," that lies at the basis of some well-known intriguing quantum effects. Such is interaction-free measurement (IFM)¹ and its more paradoxical variants like Hardy's Paradox² and the quantum liar paradox.³ Even the Aharonov–Bohm (AB) effect⁴ and weak measurement (WM)⁵ turn out to belong to this group. We next study interventions within the CI that produce some other peculiar effects. Finally, we discuss some of the conceptual issues involved. Under a greater time-resolution of the CI, some non-local phenomena turn out to be local. Momentum is conserved due to the quantum uncertainties inflicted by the particle–pointer interaction, which sets the experiment's final boundary condition.

The counterfactuality of recently proposed protocols is analyzed. A definition of “counterfactuality” is offered and it is argued that an interaction-free measurement (IFM) of the presence of an opaque object can be named “counterfactual”, while proposed “counterfactual” measurements of the absence of such objects are not counterfactual. The quantum key distribution protocols which rely only on measurements of the presence of the object are counterfactual, but quantum direct communication protocols are not. Therefore, the name “counterfactual” is not appropriate for recent “counterfactual” protocols which transfer quantum states by quantum direct communication.

We compare the roles of the Bures–Helstrom (BH) and Bogoliubov–Kubo–Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state discrimination, which we call the “thermodynamic” limit (of $N$, the number of realizations going to infinity) and the infinitesimal limit (of the separation of states tending to zero). We show that these two limits do not commute in the quantum case. Taking the infinitesimal limit first leads to the BH metric and the corresponding Cramér–Rao bound, which is widely accepted in this subject. Taking limits in the opposite order leads to the BKM metric, which results in a weaker Cramér–Rao bound. This lack of commutation of limits is a purely quantum phenomenon arising from quantum entanglement. We can exploit this phenomenon to gain a quantum advantage in state discrimination and get around the limitation imposed by the Bures–Helstrom Cramér–Rao (BHCR) bound. We propose a technologically feasible experiment with cold atoms to demonstrate the quantum advantage in the simple case of two qubits.