Related papers: Five open problems in quantum information

Five open problems in quantum information

URL: http://arxiv.org/abs/2002.03233v2
Date: Mon, 21 Dec 2020 11:39:17 GMT
Title: Five open problems in quantum information
Authors: Pawe{\l} Horodecki, {\L}ukasz Rudnicki, and Karol \.Zyczkowski
Abstract summary: We identify five selected problems in the theory of quantum information, which are rather simple to formulate. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential.
Score: 0.10427337206896375
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, were well-studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential. The first four concern existence of certain objects relevant for quantum information, namely a family of symmetric informationally complete generalized measurements in an infinite sequence of dimensions, mutually unbiased bases in dimension six, absolutely maximally entangled states for four subsystems with six levels each and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is 2-copy distillable. An award for solving each of them is announced.

Related papers

Strong Converse Exponent of Quantum Dichotomies [5.371337604556312]
We study the large-deviation behavior of quantum dichotomies and determine the exact strong converse exponent based on the purified distance. Our result is characterized by a simple optimization of quantum R'enyi information measures involving all four mutually non-commuting quantum states.
arXiv Detail & Related papers (2024-10-16T13:54:18Z)
Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
arXiv Detail & Related papers (2023-10-04T17:53:55Z)
Multipartite Entanglement: A Journey Through Geometry [0.0]
Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge. We introduce an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement.
arXiv Detail & Related papers (2023-04-06T17:59:26Z)
Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler [0.0]
We show that there is truly only em one AME state of four qutrits up to local unitary equivalence. For larger local dimensions, the number of local unitary classes of AME states is shown to be infinite. Based on this, an infinity of quantum solutions are constructed and we prove that these are not equivalent.
arXiv Detail & Related papers (2022-12-13T17:16:17Z)
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)
Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
arXiv Detail & Related papers (2022-06-30T18:00:01Z)
Quantum mappings and designs [0.0]
We provide several novel constructions useful for the comprehension of quantum mechanics. The unistochasticity problem, which relates the classical and the quantum domain, is solved in specific cases. We study cardinality as a measure of "quantumness" of quantum Latin squares and quantum Sudoku (SudoQ)
arXiv Detail & Related papers (2022-04-27T15:25:49Z)
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)
Post-Quantum Succinct Arguments: Breaking the Quantum Rewinding Barrier [73.70426431502803]
We prove that Kilian's four-message succinct argument system is post-quantum secure in the standard model. This yields the first post-quantum succinct argument system from any falsifiable assumption.
arXiv Detail & Related papers (2021-03-15T05:09:17Z)
Operational Resource Theory of Imaginarity [48.7576911714538]
We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
arXiv Detail & Related papers (2020-07-29T14:03:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.