49 research outputs found
Ontological models for quantum theory as functors
We interpret ontological models for finite-dimensional quantum theory as
functors from the category of finite-dimensional Hilbert spaces and bounded
linear maps to the category of measurable spaces and Markov kernels. This
uniformises several earlier results, that we analyse more closely: Pusey,
Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's
result rules out functors that preserve a duality between states and
measurement; Aaronson et al's result rules out functors that adhere to the
Schr\"odinger equation. We also prove that it is possible to have epistemic
functors that take values in signed Markov kernels.Comment: In Proceedings QPL 2019, arXiv:2004.1475
Computationally-Secure and Composable Remote State Preparation
We introduce a protocol between a classical polynomial-time verifier and a quantum polynomial-time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states The prover is unaware of which state he received and moreover, the verifier can check with high confidence whether the preparation was successful. The delegated preparation of single-qubit states is an elementary building block in many quantum cryptographic protocols. We expect our implementation of "random remote state preparation with verification", a functionality first defined in (Dunjko and Kashefi 2014), to be useful for removing the need for quantum communication in such protocols while keeping functionality. The main application that we detail is to a protocol for blind and verifiable delegated quantum computation (DQC) that builds on the work of (Fitzsimons and Kashefi 2018), who provided such a protocol with quantum communication. Recently, both blind an verifiable DQC were shown to be possible, under computational assumptions, with a classical polynomial-time client (Mahadev 2017, Mahadev 2018). Compared to the work of Mahadev, our protocol is more modular, applies to the measurement-based model of computation (instead of the Hamiltonian model) and is composable. Our proof of security builds on ideas introduced in (Brakerski et al. 2018)
Computationally-Secure and Composable Remote State Preparation
We introduce a protocol between a classical polynomial-time verifier and a quantum polynomial-time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states The prover is unaware of which state he received and moreover, the verifier can check with high confidence whether the preparation was successful. The delegated preparation of single-qubit states is an elementary building block in many quantum cryptographic protocols. We expect our implementation of "random remote state preparation with verification", a functionality first defined in (Dunjko and Kashefi 2014), to be useful for removing the need for quantum communication in such protocols while keeping functionality. The main application that we detail is to a protocol for blind and verifiable delegated quantum computation (DQC) that builds on the work of (Fitzsimons and Kashefi 2018), who provided such a protocol with quantum communication. Recently, both blind an verifiable DQC were shown to be possible, under computational assumptions, with a classical polynomial-time client (Mahadev 2017, Mahadev 2018). Compared to the work of Mahadev, our protocol is more modular, applies to the measurement-based model of computation (instead of the Hamiltonian model) and is composable. Our proof of security builds on ideas introduced in (Brakerski et al. 2018)
Complexity-Theoretic Limitations on Blind Delegated Quantum Computation
Blind delegation protocols allow a client to delegate a computation to a
server so that the server learns nothing about the input to the computation
apart from its size. For the specific case of quantum computation we know that
blind delegation protocols can achieve information-theoretic security. In this
paper we prove, provided certain complexity-theoretic conjectures are true,
that the power of information-theoretically secure blind delegation protocols
for quantum computation (ITS-BQC protocols) is in a number of ways constrained.
In the first part of our paper we provide some indication that ITS-BQC
protocols for delegating computations in which the client and the
server interact only classically are unlikely to exist. We first show that
having such a protocol with bits of classical communication implies
that . We conjecture that this
containment is unlikely by providing an oracle relative to which . We then show that if an ITS-BQC protocol
exists with polynomial classical communication and which allows the client to
delegate quantum sampling problems, then there exist non-uniform circuits of
size , making polynomially-sized queries to
an oracle, for computing the permanent of an matrix.
The second part of our paper concerns ITS-BQC protocols in which the client and
the server engage in one round of quantum communication and then exchange
polynomially many classical messages. First, we provide a complexity-theoretic
upper bound on the types of functions that could be delegated in such a
protocol, namely . Then, we show that
having such a protocol for delegating -hard functions implies
.Comment: Improves upon, supersedes and corrects our earlier submission, which
previously included an error in one of the main theorem
Robust verification of quantum computation
Quantum computers promise to offer a considerable speed-up in solving certain
problems, compared to the best classical algorithms. In many instances, the gap
between quantum and classical running times is conjectured to be exponential.
While this is great news for those applications where quantum computers would
provide such an advantage, it also raises a significant challenge: how can classical
computers verify the correctness of quantum computations? In attempting to
answer this question, a number of protocols have been developed in which a
classical client (referred to as verifier) can interact with one or more quantum
servers (referred to as provers) in order to certify the correctness of a quantum
computation performed by the server(s). These protocols are of one of two types:
either there are multiple non-communicating provers, sharing entanglement, and
the verifier is completely classical; or, there is a single prover and the classical
verifier has a device for preparing or measuring quantum states. The latter type
of protocols are, arguably, more relevant to near term quantum computers, since
having multiple quantum computers that share a large amount of entanglement
is, from a technological standpoint, extremely challenging.
Before the realisation of practical single-prover protocols, a number of challenges
need to be addressed: how robust are these protocols to noise on the
verifier's device? Can the protocols be made fault-tolerant without significantly
increasing the requirements of the verifier? How do we know that the verifier's
device is operating correctly? Could this device be eliminated completely, thus
having a protocol with a fully classical verifier and a single quantum prover? Our
work attempts to provide answers to these questions.
First, we consider a single-prover verification protocol developed by Fitzsimons
and Kashefi and show that this protocol is indeed robust with respect to
deviations on the quantum state prepared by the verifier. We show that this
is true even if those deviations are the result of a correlation with the prover's
system. We then use this result to give a verification protocol which is device-
independent. The protocol consists of a verifier with a measurement device and
a single prover. Device-independence means that the verifier need not trust the
measurement device (nor the prover) which can be assumed to be fully malicious
(though not communicating with the prover). A key element in realising
this protocol is a robust technique of Reichardt, Unger and Vazirani for testing,
using non-local correlations, that two untrusted devices share a large number of
entangled states. This technique is referred to as rigidity of non-local correlations.
Our second result is to prove a rigidity result for a type of quantum correlations
known as steering correlations. To do this, we first show that steering correlations
can be used in order to certify maximally entangled states, in a setting in which
each test is independent of the previous one. We also show that the fidelity with
which we characterise the state, in this specific test, is optimal. We then improve
the previous result by removing the independence assumption. This then leads
to our desired rigidity result. We make use of it, in a similar fashion to the
device-independent case, in order to give a verification protocol that is one-sided
device-independent. The importance of this application is to show how different
trust assumptions affect the efficiency of the protocol.
Next, we describe a protocol for fault-tolerantly verifying quantum computations,
with minimal "quantum requirements" for the verifier. Specifically, the
verifier only requires a device for measuring single-qubit states. Both this device,
and the prover's operations are assumed to be prone to errors. We show that
under standard assumptions about the error model, it is possible to achieve verification of quantum computation using fault-tolerant principles. As a proof of
principle, and to better illustrate the inner workings of the protocol, we describe
a toy implementation of the protocol in a quantum simulator, and present the
results we obtained, when running it for a small computation.
Finally, we explore the possibility of having a verification protocol, with a
classical verifier and a single prover, such that the prover is blind with respect
to the verifier's computation. We give evidence that this is not possible. In fact,
our result is only concerned with blind quantum computation with a classical
client, and uses complexity theoretic results to argue why it is improbable for
such a protocol to exist. We then use these complexity theoretic techniques to
show that a client, with the ability to prepare and send quantum states to a
quantum server, would not be able to delegate arbitrary NP problems to that
server. In other words, even a client with quantum capabilities cannot exploit
those capabilities to delegate the computation of NP problems, while keeping
the input, to that computation, private. This is again true, provided certain
complexity theoretic conjectures are true
Nonlocality under Computational Assumptions
Nonlocality and its connections to entanglement are fundamental features of
quantum mechanics that have found numerous applications in quantum information
science. A set of correlations is said to be nonlocal if it cannot be
reproduced by spacelike-separated parties sharing randomness and performing
local operations. An important practical consideration is that the runtime of
the parties has to be shorter than the time it takes light to travel between
them. One way to model this restriction is to assume that the parties are
computationally bounded. We therefore initiate the study of nonlocality under
computational assumptions and derive the following results:
(a) We define the set (not-efficiently-local) as consisting of
all bipartite states whose correlations arising from local measurements cannot
be reproduced with shared randomness and \emph{polynomial-time} local
operations.
(b) Under the assumption that the Learning With Errors problem cannot be
solved in \emph{quantum} polynomial-time, we show that
, where is the set of \emph{all}
bipartite entangled states (pure and mixed). This is in contrast to the
standard notion of nonlocality where it is known that some entangled states,
e.g. Werner states, are local. In essence, we show that there exist (efficient)
local measurements producing correlations that cannot be reproduced through
shared randomness and quantum polynomial-time computation.
(c) We prove that if unconditionally, then
. In other words, the ability to certify all
bipartite entangled states against computationally bounded adversaries gives a
non-trivial separation of complexity classes.
(d) Using (c), we show that a certain natural class of 1-round delegated
quantum computation protocols that are sound against provers
cannot exist.Comment: 65 page
A new approach to balance dental fear and anxiety by using BachTM Flower Therapy
Treatments in dentistry currently consist of an interdisciplinary approach, including (but not necessarily limited to) the holistic perspective. The different fields of allopathic and complementary medicine are used together to ensure not only a high-quality restorative treatment, but also to provide patients with psychological and emotional support. This perspective also applies to dental anxiety, which consists of complex (emotional, vegetative and psychomotor) manifestations. One of the most well-known complementary therapies for reducing dental fear and anxiety is BachTM Flower Therapy. Even if the mechanism of action of this therapy is not yet scientifically documented, notable results have been and continue to be reported in the literature in several clinical studies on patients with dental diseases. It is indicated for both adults and children, in the latter when they go through major biological changes, such as primary and permanent dentition. As a conclusion, BachTM flower therapy is effective and complementary to dental treatments applied to patients, by reducing stress, anxiety, as well as creating a climate of peace, trust and confidence, both for the patient and the doctor. In addition, it is a relatively accessible and cheap form of care, with no significant adverse effects noted so far
Management of a flare up case after endodontic treatment procedure
A flare-up is defined as a pain and/or swelling of the soft tissues that occurs within a few hous or a few days following the root canal treatment. In some cases, the flare-ups can apear after the finishing of the root canal treatment, due to the penetration or development of the microorganisms into the root canal. The pain felt by the patient depends on the extent of the periradicular tissue injury, its severity and intensity of the inflammatory imune response. The article discusses the microbial irritation of apical periodontal tissue caused by insufficient instrumentation and filling of the root canals, factors that lead to failure of the outcome of root canals treatment
The causes of adhesive direct dental restorations failures
The modern dental caries adhesive direct restoration requires a working protocol that includes stages and techniques that must be strictly followed to ensure the correct morphological and functional reconstruction, as well as an increased longevity of the restoration and implicitly of the respective tooth in the oral cavity. Failures in achieving these goals are represented by the occurrence of recurrent caries, secondary or residual caries, coronary fractures, leading to pulpal and periodontal complications. They can be due to both incorrect therapeutic maneuvers and other causes, for which the dentist is not responsible, such as manufacturing defects of dental materials that are not visible during inspection or the patient's attitude towards oral hygiene