278 research outputs found
Optimal measurement strategies for the trine states with arbitrary prior probabilities
We investigate the optimal measurement strategy for state discrimination of the trine ensemble of qubit states prepared with arbitrary prior probabilities. Our approach generates the minimum achievable probability of error and also the maximum confidence strategy. Although various cases with symmetry have been considered and solution techniques put forward in the literature, to our knowledge this is only the second such closed form, analytical, arbitrary prior, example available for the minimum-error figure of merit, after the simplest and well-known two-state example
Optimal measurement strategies for the trine states with arbitrary prior probabilities
We investigate the optimal measurement strategy for state discrimination of
the trine ensemble of qubit states prepared with arbitrary prior probabilities.
Our approach generates the minimum achievable probability of error and also the
maximum confidence strategy. Although various cases with symmetry have been
considered and solution techniques put forward in the literature, to our
knowledge this is only the second such closed form, analytical, arbitrary
prior, example available for the minimum-error figure of merit, after the
simplest and well-known two-state example
Optimal discrimination of quantum states
Quantum state discrimination is a fundamental task in the field of quantum communication and quantum information theory. Unless the states to be discriminated are mutually orthogonal, there will be some error in any attempt to determine which state was sent. Several strategies to optimally discriminate between quantum states exist, each maximising some figure of merit. In this thesis we mainly investigate the minimum-error strategy, in which the probability of correctly guessing the signal state is maximised. We introduce a method for constructing the optimal Positive-Operator Valued Measure (POVM) for this figure of merit, which is applicable for arbitrary states and arbitrary prior probabilities. We then use this method to solve minimum-error state discrimination for the so-called trine states with arbitrary prior probabilities - the first such general solution for a set of quantum states since the two-state case was solved when the problem of state discrimination was first introduced. We also investigate the difference between local and global measurements for a bipartite ensemble of states, and find that in certain circumstances the local measurement is superior. We conclude by finding a bipartite analogue to the Helstrom conditions, which indicate when a POVM satisfies the minimum-error criteria
An Analysis of Mutually Dispersive Brown Symbols for Non-Linear Ambiguity Suppression
This thesis significantly advances research towards the implementation of optimal Non-linear Ambiguity Suppression (NLS) waveforms by analyzing the Brown theorem. The Brown theorem is reintroduced with the use of simplified linear algebraic notation. A methodology for Brown symbol design and digitization is provided, and the concept of dispersive gain is introduced. Numerical methods are utilized to design, synthesize, and analyze Brown symbol performance. The theoretical performance in compression and dispersion of Brown symbols is demonstrated and is shown to exhibit significant improvement compared to discrete codes. As a result of this research a process is derived for the design of optimal mutually dispersive symbols for any sized family. In other words, the limitations imposed by conjugate LFM are overcome using NLS waveforms that provide an effective-fold increase in radar unambiguous range. This research effort has taken a theorem from its infancy, validated it analytically, simplified it algebraically, tested it for realizability, and now provides a means for the synthesis and digitization of pulse coded waveforms that generate an N-fold increase in radar effective unambiguous range. Peripherally, this effort has motivated many avenues of future research
Optimal Lossless Dynamic Quantum Huffman Block Encoding
In this article we present an adaptation of the quantum Huffman encoding
which was introduced in [IEEE Transactions on information theory 46.4 (2000):
1644-1649] and was studied in [Scientific Reports 7.1 (2017): 14765]. Our
adaptation gives a block encoding as it is applied successively to encode one
block after the other. It is also a dynamic encoding because it is updated at
every block. We prove that our encoding gives the optimal average codeword
length over any other dynamic block encoding with a common jointly orthonormal
sequence of length codewords
Quantum Cloning Machines and the Applications
No-cloning theorem is fundamental for quantum mechanics and for quantum
information science that states an unknown quantum state cannot be cloned
perfectly. However, we can try to clone a quantum state approximately with the
optimal fidelity, or instead, we can try to clone it perfectly with the largest
probability. Thus various quantum cloning machines have been designed for
different quantum information protocols. Specifically, quantum cloning machines
can be designed to analyze the security of quantum key distribution protocols
such as BB84 protocol, six-state protocol, B92 protocol and their
generalizations. Some well-known quantum cloning machines include universal
quantum cloning machine, phase-covariant cloning machine, the asymmetric
quantum cloning machine and the probabilistic quantum cloning machine etc. In
the past years, much progress has been made in studying quantum cloning
machines and their applications and implementations, both theoretically and
experimentally. In this review, we will give a complete description of those
important developments about quantum cloning and some related topics. On the
other hand, this review is self-consistent, and in particular, we try to
present some detailed formulations so that further study can be taken based on
those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published
online
Quantum statistical inference and communication
This thesis studies the limits on the performances of inference tasks with quantum data
and quantum operations. Our results can be divided in two main parts.
In the first part, we study how to infer relative properties of sets of quantum states,
given a certain amount of copies of the states. We investigate the performance of optimal
inference strategies according to several figures of merit which quantifies the precision of
the inference. Since we are not interested in obtaining a complete reconstruction of the
states, optimal strategies do not require to perform quantum tomography. In particular,
we address the following problems:
- We evaluate the asymptotic error probabilities of optimal learning machines for
quantum state discrimination. Here, a machine receives a number of copies of a
pair of unknown states, which can be seen as training data, together with a test
system which is initialized in one of the states of the pair with equal probability.
The goal is to implement a measurement to discriminate in which state the test
system is, minimizing the error probability. We analyze the optimal strategies for
a number of different settings, differing on the prior incomplete information on the
states available to the agent.
- We evaluate the limits on the precision of the estimation of the overlap between two
unknown pure states, given N and M copies of each state. We find an asymptotic
expansion of a Fisher information associated with the estimation problem, which
gives a lower bound on the mean square error of any estimator. We compute the
minimum average mean square error for random pure states, and we evaluate the
effect of depolarizing noise on qubit states. We compare the performance of the
optimal estimation strategy with the performances of other intuitive strategies,
such as the swap test and measurements based on estimating the states.
- We evaluate how many samples from a collection of N d-dimensional states are
necessary to understand with high probability if the collection is made of identical
states or they differ more than a threshold according to a motivated closeness
measure. The access to copies of the states in the collection is given as follows:
each time the agent ask for a copy of the states, the agent receives one of the states with some fixed probability, together with a different label for each state in the collection. We prove that the problem can be solved with O(pNd=2) copies, and
that this scaling is optimal up to a constant independent on d;N; .
In the second part, we study optimal classical and quantum communication rates for
several physically motivated noise models.
- The quantum and private capacities of most realistic channels cannot be evaluated
from their regularized expressions. We design several degradable extensions
for notable channels, obtaining upper bounds on the quantum and private capacities
of the original channels. We obtain sufficient conditions for the degradability
of flagged extensions of channels which are convex combination of other channels.
These sufficient conditions are easy to verify and simplify the construction of
degradable extensions.
- We consider the problem of transmitting classical information with continuous variable
systems and an energy constraint, when it is impossible to maintain a shared
reference frame and in presence of losses. At variance with phase-insensitive noise
models, we show that, in some regimes, squeezing improves the communication
rates with respect to coherent state sources and with respect to sources producing
up to two-photon Fock states. We give upper and lower bounds on the optimal
coherent state rate and show that using part of the energy to repeatedly restore a
phase reference is strictly suboptimal for high energies
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
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