Are the 'weak measurements' really measurements?

Weak measurements can be seen as an attempt at answering the 'Which way?' question without destroying interference between the pathways involved. Unusual mean values obtained in such measurements represent the response of a quantum system to this 'forbidden' question, in which the 'true' composition of virtual pathways is hidden from the observer. Such values indicate a failure of a measurement where the uncertainty principle says it must fail, rather than provide an additional insight into physical reality

Universality of quantum Brownian motion

Are Markovian master equations for quantum Brownian motion independent of model assumptions used in the derivation and, thus, universal? With the aim of answering this question, we use a random band-matrix model for the system-bath interaction to derive Markovian master equations for the time evolution of one-dimensional quantum systems weakly coupled to a heat bath. We study in detail two simple systems, the harmonic oscillator and the two-level system. Our results are in complete agreement with those of earlier models, like the Caldeira-Legget model and, in the large-band limit, with the Agarwal equations (both with and without rotating-wave approximation). This proves the universality of these master equations.Comment: 24 page

Numerical Evidence for Robustness of Environment-Assisted Quantum Transport

Recent theoretical studies show that decoherence process can enhance transport efficiency in quantum systems. This effect is known as environment-assisted quantum transport (ENAQT). The role of ENAQT in optimal quantum transport is well investigated, however, it is less known how robust ENAQT is with respect to variations in the system or its environment characteristic. Toward answering this question, we simulated excitonic energy transfer in Fenna-Matthews-Olson (FMO) photosynthetic complex. We found that ENAQT is robust with respect to many relevant parameters of environmental interactions and Frenkel-exciton Hamiltonian including reorganization energy, bath frequency cutoff, temperature, and initial excitations, dissipation rate, trapping rate, disorders, and dipole moments orientations. Our study suggests that the ENAQT phenomenon can be exploited in robust design of highly efficient quantum transport systems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.481

An efficient quantum parallel repetition theorem and applications

We prove a tight parallel repetition theorem for $3$-message computationally-secure quantum interactive protocols between an efficient challenger and an efficient adversary. We also prove under plausible assumptions that the security of $4$-message computationally secure protocols does not generally decrease under parallel repetition. These mirror the classical results of Bellare, Impagliazzo, and Naor [BIN97]. Finally, we prove that all quantum argument systems can be generically compiled to an equivalent $3$-message argument system, mirroring the transformation for quantum proof systems [KW00, KKMV07]. As immediate applications, we show how to derive hardness amplification theorems for quantum bit commitment schemes (answering a question of Yan [Yan22]), EFI pairs (answering a question of Brakerski, Canetti, and Qian [BCQ23]), public-key quantum money schemes (answering a question of Aaronson and Christiano [AC13]), and quantum zero-knowledge argument systems. We also derive an XOR lemma [Yao82] for quantum predicates as a corollary

Does Quantum Mechanics Need Interpretation?

Since the beginning, quantum mechanics has raised major foundational and interpretative problems. Foundational research has been an important factor in the development of quantum cryptography, quantum information theory and, perhaps one day, practical quantum computers. Many believe that, in turn, quantum information theory has bearing on foundational research. This is largely related to the so-called epistemic view of quantum states, which maintains that the state vector represents information on a system and has led to the suggestion that quantum theory needs no interpretation. I will argue that this and related approaches fail to take into consideration two different explanatory functions of quantum mechanics, namely that of accounting for classically unexplainable correlations between classical phenomena and that of explaining the microscopic structure of classical objects. If interpreting quantum mechanics means answering the question, "How can the world be for quantum mechanics to be true?", there seems to be no way around it.Comment: Based on quant-ph/0510120, quant-ph/0502049 and quant-ph/040512

Recovering hidden Bloch character: Unfolding Electrons, Phonons, and Slabs

For a quantum state, or classical harmonic normal mode, of a system of spatial periodicity "R", Bloch character is encoded in a wavevector "K". One can ask whether this state has partial Bloch character "k" corresponding to a finer scale of periodicity "r". Answering this is called "unfolding." A theorem is proven that yields a mathematically clear prescription for unfolding, by examining translational properties of the state, requiring no "reference states" or basis functions with the finer periodicity (r,k). A question then arises, how should one assign partial Bloch character to a state of a finite system? A slab, finite in one direction, is used as the example. Perpendicular components k_z of the wavevector are not explicitly defined, but may be hidden in the state (and eigenvector |i>.) A prescription for extracting k_z is offered and tested. An idealized silicon (111) surface is used as the example. Slab-unfolding reveals surface-localized states and resonances which were not evident from dispersion curves alone.Comment: 11 pages, 7 figure

Quantum Stochastic Processes and Quantum Many-Body Physics

This dissertation investigates the theory of quantum stochastic processes and its applications in quantum many-body physics. The main goal is to analyse complexity-theoretic aspects of both static and dynamic properties of physical systems modelled by quantum stochastic processes. The thesis consists of two parts: the first one addresses the computational complexity of certain quantum and classical divisibility questions, whereas the second one addresses the topic of Hamiltonian complexity theory. In the divisibility part, we discuss the question whether one can efficiently sub-divide a map describing the evolution of a system in a noisy environment, i.e. a CPTP- or stochastic map for quantum and classical processes, respectively, and we prove that taking the nth root of a CPTP or stochastic map is an NP-complete problem. Furthermore, we show that answering the question whether one can divide up a random variable $X$ into a sum of $n$ iid random variables $Y_i$, i.e. $X=\sum_{i=1}^n Y_i$, is poly-time computable; relaxing the iid condition renders the problem NP-hard. In the local Hamiltonian part, we study computation embedded into the ground state of a many-body quantum system, going beyond "history state" constructions with a linear clock. We first develop a series of mathematical techniques which allow us to study the energy spectrum of the resulting Hamiltonian, and extend classical string rewriting to the quantum setting. This allows us to construct the most physically-realistic QMAEXP-complete instances for the LOCAL HAMILTONIAN problem (i.e. the question of estimating the ground state energy of a quantum many-body system) known to date, both in one- and three dimensions. Furthermore, we study weighted versions of linear history state constructions, allowing us to obtain tight lower and upper bounds on the promise gap of the LOCAL HAMILTONIAN problem in various cases. We finally study a classical embedding of a Busy Beaver Turing Machine into a low-dimensional lattice spin model, which allows us to dictate a transition from a purely classical phase to a Toric Code phase at arbitrarily large and potentially even uncomputable system sizes

On the sampling complexity of open quantum systems

Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in their efficient simulation. However, direct classical simulation quickly becomes intractable with coupling to an environment whose effective dimension grows exponentially. This raises the question: can quantum computers help model these complex dynamics? A first step in answering this question requires understanding the computational complexity of this task. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state using a computational model known as the process tensor framework. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. The complexity of multi-time sampling, which is an important and interesting problem in its own right, contains the complexity of master equations and stochastic maps as a special case. Our results show how the complexity of the underlying quantum stochastic process corresponds to the complexity of the associated family of master equations for the dynamics. We present both analytical and numerical examples whose multi-time sampling is as complex as sampling from a many-body state that is classically hard. This also implies that the corresponding family of master equations are classically hard. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics

A Quantum Many-body Wave Function Inspired Language Modeling Approach

The recently proposed quantum language model (QLM) aimed at a principled approach to modeling term dependency by applying the quantum probability theory. The latest development for a more effective QLM has adopted word embeddings as a kind of global dependency information and integrated the quantum-inspired idea in a neural network architecture. While these quantum-inspired LMs are theoretically more general and also practically effective, they have two major limitations. First, they have not taken into account the interaction among words with multiple meanings, which is common and important in understanding natural language text. Second, the integration of the quantum-inspired LM with the neural network was mainly for effective training of parameters, yet lacking a theoretical foundation accounting for such integration. To address these two issues, in this paper, we propose a Quantum Many-body Wave Function (QMWF) inspired language modeling approach. The QMWF inspired LM can adopt the tensor product to model the aforesaid interaction among words. It also enables us to reveal the inherent necessity of using Convolutional Neural Network (CNN) in QMWF language modeling. Furthermore, our approach delivers a simple algorithm to represent and match text/sentence pairs. Systematic evaluation shows the effectiveness of the proposed QMWF-LM algorithm, in comparison with the state of the art quantum-inspired LMs and a couple of CNN-based methods, on three typical Question Answering (QA) datasets.Comment: 10 pages,4 figures,CIK