84 research outputs found
Transformations between symmetric sets of quantum states
We investigate probabilistic transformations of quantum states from a
`source' set to a `target' set of states. Such transforms have many
applications. They can be used for tasks which include state-dependent cloning
or quantum state discrimination, and as interfaces between systems whose
information encodings are not related by a unitary transform, such as
continuous-variable systems and finite-dimensional systems. In a probabilistic
transform, information may be lost or leaked, and we explain the concepts of
leak and redundancy. Following this, we show how the analysis of probabilistic
transforms significantly simplifies for symmetric source and target sets of
states. In particular, we give a simple linear program which solves the task of
finding optimal transforms, and a method of characterizing the introduced leak
and redundancy in information-theoretic terms. Using the developed techniques,
we analyse a class of transforms which convert coherent states with information
encoded in their relative phase to symmetric qubit states. Each of these sets
of states on their own appears in many well studied quantum information
protocols. Finally, we suggest an asymptotic realization based on quantum
scissors.Comment: 10 pages; 5 figure
Ideal quantum protocols in the non-ideal physical world
The development of quantum protocols from conception to experimental realizations is one of
the main sources of the stimulating exchange between fundamental and experimental research
characteristic to quantum information processing. In this thesis we contribute to the development
of two recent quantum protocols, Universal Blind Quantum Computation (UBQC) and Quantum
Digital Signatures (QDS). UBQC allows a client to delegate a quantum computation to a more
powerful quantum server while keeping the input and computation private. We analyse the resilience
of the privacy of UBQC under imperfections. Then, we introduce approximate blindness
quantifying any compromise to privacy, and propose a protocol which enables arbitrary levels of
security despite imperfections. Subsequently, we investigate the adaptability of UBQC to alternative
implementations with practical advantages. QDS allow a party to send a message to other
parties which cannot be forged, modified or repudiated. We analyse the security properties of a
first proof-of-principle experiment of QDS, implemented in an optical system. We estimate the
security failure probabilities of our system as a function of protocol parameters, under all but the
most general types of attacks. Additionally, we develop new techniques for analysing transformations
between symmetric sets of states, utilized not only in the security proofs of QDS but in
other applications as well
Quantum-enhanced Secure Delegated Classical Computing
We present a quantumly-enhanced protocol to achieve unconditionally secure
delegated classical computation where the client and the server have both
limited classical and quantum computing capacity. We prove the same task cannot
be achieved using only classical protocols. This extends the work of Anders and
Browne on the computational power of correlations to a security setting.
Concretely, we present how a client with access to a non-universal classical
gate such as a parity gate could achieve unconditionally secure delegated
universal classical computation by exploiting minimal quantum gadgets. In
particular, unlike the universal blind quantum computing protocols, the
restriction of the task to classical computing removes the need for a full
universal quantum machine on the side of the server and makes these new
protocols readily implementable with the currently available quantum technology
in the lab
Neural Network Operations and Susuki-Trotter evolution of Neural Network States
It was recently proposed to leverage the representational power of artificial
neural networks, in particular Restricted Boltzmann Machines, in order to model
complex quantum states of many-body systems [Science, 355(6325), 2017]. States
represented in this way, called Neural Network States (NNSs), were shown to
display interesting properties like the ability to efficiently capture
long-range quantum correlations. However, identifying an optimal neural network
representation of a given state might be challenging, and so far this problem
has been addressed with stochastic optimization techniques. In this work we
explore a different direction. We study how the action of elementary quantum
operations modifies NNSs. We parametrize a family of many body quantum
operations that can be directly applied to states represented by Unrestricted
Boltzmann Machines, by just adding hidden nodes and updating the network
parameters. We show that this parametrization contains a set of universal
quantum gates, from which it follows that the state prepared by any quantum
circuit can be expressed as a Neural Network State with a number of hidden
nodes that grows linearly with the number of elementary operations in the
circuit. This is a powerful representation theorem (which was recently obtained
with different methods) but that is not directly useful, since there is no
general and efficient way to extract information from this unrestricted
description of quantum states. To circumvent this problem, we propose a
step-wise procedure based on the projection of Unrestricted quantum states to
Restricted quantum states. In turn, two approximate methods to perform this
projection are discussed. In this way, we show that it is in principle possible
to approximately optimize or evolve Neural Network States without relying on
stochastic methods such as Variational Monte Carlo, which are computationally
expensive
- …