599 research outputs found
Performance and structure of single-mode bosonic codes
The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit
in an oscillator has recently been followed by cat- and binomial-code
proposals. Numerically optimized codes have also been proposed, and we
introduce new codes of this type here. These codes have yet to be compared
using the same error model; we provide such a comparison by determining the
entanglement fidelity of all codes with respect to the bosonic pure-loss
channel (i.e., photon loss) after the optimal recovery operation. We then
compare achievable communication rates of the combined encoding-error-recovery
channel by calculating the channel's hashing bound for each code. Cat and
binomial codes perform similarly, with binomial codes outperforming cat codes
at small loss rates. Despite not being designed to protect against the
pure-loss channel, GKP codes significantly outperform all other codes for most
values of the loss rate. We show that the performance of GKP and some binomial
codes increases monotonically with increasing average photon number of the
codes. In order to corroborate our numerical evidence of the cat/binomial/GKP
order of performance occurring at small loss rates, we analytically evaluate
the quantum error-correction conditions of those codes. For GKP codes, we find
an essential singularity in the entanglement fidelity in the limit of vanishing
loss rate. In addition to comparing the codes, we draw parallels between
binomial codes and discrete-variable systems. First, we characterize one- and
two-mode binomial as well as multi-qubit permutation-invariant codes in terms
of spin-coherent states. Such a characterization allows us to introduce check
operators and error-correction procedures for binomial codes. Second, we
introduce a generalization of spin-coherent states, extending our
characterization to qudit binomial codes and yielding a new multi-qudit code.Comment: 34 pages, 11 figures, 4 tables. v3: published version. See related
talk at https://absuploads.aps.org/presentation.cfm?pid=1351
Multi-party quantum private comparison based on entanglement swapping of Bell entangled states within d-level quantum system
In this paper, a multi-party quantum private comparison (MQPC) scheme is
suggested based on entanglement swapping of Bell entangled states within
d-level quantum system, which can accomplish the equality comparison of secret
binary sequences from n users via one execution of scheme. Detailed security
analysis shows that both the outside attack and the participant attack are
ineffective. The suggested scheme needn't establish a private key among n users
beforehand through the quantum key distribution (QKD) method to encrypt the
secret binary sequences. Compared with previous MQPC scheme based on d-level
Cat states and d-level Bell entangled states, the suggested scheme has distinct
advantages on quantum resource, quantum measurement of third party (TP) and
qubit efficiency.Comment: 8 pages, 1 figure, 1 tabl
Multi-party quantum private comparison of size relationship with two third parties based on d-dimensional Bell states
In this paper, we put forward a multi-party quantum private comparison (MQPC)
protocol with two semi-honest third parties (TPs) by adopting d-dimensional
Bell states, which can judge the size relationship of private integers from
more than two users within one execution of protocol. Each TP is permitted to
misbehave on her own but cannot collude with others. In the proposed MQPC
protocol, TPs are only required to apply d-dimensional single-particle
measurements rather than d-dimensional Bell state measurements. There are no
quantum entanglement swapping and unitary operations required in the proposed
MQPC protocol. The security analysis validates that the proposed MQPC protocol
can resist both the outside attacks and the participant attacks. The proposed
MQPC protocol is adaptive for the case that users want to compare the size
relationship of their private integers under the control of two supervisors.
Furthermore, the proposed MQPC protocol can be used in the strange user
environment, because there are not any communication and pre-shared key between
each pair of users.Comment: 15 pages, 1 figure, 1 tabl
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Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
We present a systematic study of the geometric R\'enyi divergence (GRD), also
known as the maximal R\'enyi divergence, from the point of view of quantum
information theory. We show that this divergence, together with its extension
to channels, has many appealing structural properties. For example we prove a
chain rule inequality that immediately implies the "amortization collapse" for
the geometric R\'enyi divergence, addressing an open question by Berta et al.
[arXiv:1808.01498, Equation (55)] in the area of quantum channel
discrimination. As applications, we explore various channel capacity problems
and construct new channel information measures based on the geometric R\'enyi
divergence, sharpening the previously best-known bounds based on the
max-relative entropy while still keeping the new bounds single-letter
efficiently computable. A plethora of examples are investigated and the
improvements are evident for almost all cases
Semi-quantum private comparison and its generalization to the key agreement, summation, and anonymous ranking
Semi-quantum protocols construct connections between quantum users and
``classical'' users who can only perform certain ``classical'' operations. In
this paper, we present a new semi-quantum private comparison protocol based on
entangled states and single particles, which does not require pre-shared keys
between the ``classical'' users to guarantee the security of their private
data. By utilizing multi-particle entangled states and single particles, our
protocol can be easily extended to multi-party scenarios to meet the
requirements of multiple ``classical'' users who want to compare their private
data. The security analysis shows that the protocol can effectively prevent
attacks from outside eavesdroppers and adversarial participants. Besides, we
generalize the proposed protocol to other semi-quantum protocols such as
semi-quantum key agreement, semi-quantum summation, and semi-quantum anonymous
ranking protocols. We compare and discuss the proposed protocols with previous
similar protocols. The results show that our protocols satisfy the demands of
their respective counterparts separately. Therefore, our protocols have a wide
range of application scenarios.Comment: 19 pages 5 table
Bipartite Quantum Interactions: Entangling and Information Processing Abilities
The aim of this thesis is to advance the theory behind quantum information
processing tasks, by deriving fundamental limits on bipartite quantum
interactions and dynamics, which corresponds to an underlying Hamiltonian that
governs the physical transformation of a two-body open quantum system. The goal
is to determine entangling abilities of such arbitrary bipartite quantum
interactions. Doing so provides fundamental limitations on information
processing tasks, including entanglement distillation and secret key
generation, over a bipartite quantum network. We also discuss limitations on
the entropy change and its rate for dynamics of an open quantum system weakly
interacting with the bath. We introduce a measure of non-unitarity to
characterize the deviation of a doubly stochastic quantum process from a
noiseless evolution.
Next, we introduce information processing tasks for secure read-out of
digital information encoded in read-only memory devices against adversaries of
varying capabilities. The task of reading a memory device involves the
identification of an interaction process between probe system, which is in
known state, and the memory device. Essentially, the information is stored in
the choice of channels, which are noisy quantum processes in general and are
chosen from a publicly known set. Hence, it becomes pertinent to securely read
memory devices against scrutiny of an adversary. In particular, for a secure
read-out task called private reading when a reader is under surveillance of a
passive eavesdropper, we have determined upper bounds on its performance. We do
so by leveraging the fact that private reading of digital information stored in
a memory device can be understood as secret key agreement via a specific kind
of bipartite quantum interaction.Comment: PhD Thesis (minor revision). Also available at:
https://digitalcommons.lsu.edu/gradschool_dissertations/4717
Quantum optics of a Bose-Einstein condensate coupled to a quantized light field
We consider the interaction between a Bose-Einstein condensate and a
single-mode quantized light field in the presence of a strong far off-resonant
pump laser. The dynamics is characterized by an exponential instability, hence
the system acts as an atom-photon parametric amplifier. Triggered by a small
injected probe field, or simply by quantum noise, entangled atom-photon pairs
are created which exhibit non-classical correlations similar to those seen
between photons in the optical parametric amplifier. In addition, the quantum
statistics of the matter and light fields depend strongly on the initial state
which triggers the amplifier. Thus by preparing different initial states of the
light field, one can generate matter waves in a variety of quantum states,
demonstrating optical control over the quantum statistics of matter waves
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
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