Asymmetric cloning in quantum information theory
- URL: http://arxiv.org/abs/2309.17229v1
- Date: Fri, 29 Sep 2023 13:27:45 GMT
- Title: Asymmetric cloning in quantum information theory
- Authors: Denis Rochette
- Abstract summary: The research explores Schur-Weyl duality and its extensions, which allow efficient representation and manipulation of quantum systems.
A primary application of Schur-Weyl duality is the quantum cloning problem, which is studied for both the $1 to 2$ and the more general $1 to N$ cases.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This thesis investigates quantum cloning and related quantum entanglement
problems using core concepts of representation theory, in particular those
associated with the symmetric group. The research explores Schur-Weyl duality
and its extensions, which allow efficient representation and manipulation of
quantum systems, serving as a valuable tool for quantum information theory. A
primary application of Schur-Weyl duality is the quantum cloning problem, which
is studied for both the $1 \to 2$ and the more general $1 \to N$ cases,
providing new insights into the constraints imposed by the no-cloning theorem.
The investigation extends to a more general quantum entanglement problem on a
complete graph.
Related papers
- Proposals for ruling out the real quantum theories in an
entanglement-swapping quantum network with causally independent sources [4.878380852633981]
We study the discrimination between the real and complex quantum theories with an entanglement swapping scenario.
We find a proposal with optimal coefficients of the correlation function which could give a larger discrimination between the real and quantum theories.
arXiv Detail & Related papers (2023-12-22T09:22:09Z) - A simple formulation of no-cloning and no-hiding that admits efficient
and robust verification [0.0]
Incompatibility is a feature of quantum theory that sets it apart from classical theory.
The no-hiding theorem is another such instance that arises in the context of the black-hole information paradox.
We formulate both of these fundamental features of quantum theory in a single form that is amenable to efficient verification.
arXiv Detail & Related papers (2023-03-05T12:48:11Z) - Entanglement measures for two-particle quantum histories [0.0]
We prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1.
We then illustrate the non-classical nature of entangled histories with the use of Hardy's overlapping interferometers.
arXiv Detail & Related papers (2022-12-14T20:48:36Z) - Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
We study the problem of designing worst-case to average-case reductions for quantum algorithms.
We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
arXiv Detail & Related papers (2022-12-06T22:01:49Z) - Theory of Quantum Generative Learning Models with Maximum Mean
Discrepancy [67.02951777522547]
We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs)
We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution.
Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
arXiv Detail & Related papers (2022-05-10T08:05:59Z) - Efficient Bipartite Entanglement Detection Scheme with a Quantum
Adversarial Solver [89.80359585967642]
Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits.
We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
arXiv Detail & Related papers (2022-03-15T09:46:45Z) - A thorough introduction to non-relativistic matrix mechanics in
multi-qudit systems with a study on quantum entanglement and quantum
quantifiers [0.0]
This article provides a deep and abiding understanding of non-relativistic matrix mechanics.
We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators.
We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
arXiv Detail & Related papers (2021-09-14T05:06:47Z) - Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems.
By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
arXiv Detail & Related papers (2021-08-03T17:49:09Z) - Perturbation Theory for Quantum Information [1.2792576041526287]
We develop theories for two classes of quantum state perturbations, perturbations that preserve the vector support of the original state and perturbations that extend the support beyond the original state.
We apply our perturbation theories to find simple expressions for four of the most important quantities in quantum information theory.
arXiv Detail & Related papers (2021-06-10T06:49:41Z) - Experimental Validation of Fully Quantum Fluctuation Theorems Using
Dynamic Bayesian Networks [48.7576911714538]
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems.
We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
arXiv Detail & Related papers (2020-12-11T12:55:17Z) - Quantum Statistical Complexity Measure as a Signalling of Correlation
Transitions [55.41644538483948]
We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions.
We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain.
We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
arXiv Detail & Related papers (2020-02-05T00:45:21Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.