Related papers: On the Complexity of Computing Zero-Error and Hole…
We show the equivalence of two different notions of quantum channel capacity: that which uses the entanglement fidelity as its criterion of success in transmission, and that which uses the minimum fidelity of pure states in a subspace of…
Quantum satisfiability is a constraint satisfaction problem that generalizes classical boolean satisfiability. In the quantum k-SAT problem, each constraint is specified by a k-local projector and is satisfied by any state in its nullspace.…
Matrix completion is a fundamental problem that comes up in a variety of applications like the Netflix problem, collaborative filtering, computer vision, and crowdsourcing. The goal of the problem is to recover a k-by-n unknown matrix from…
Several relations between the Holevo capacity and the entanglement-assisted classical capacity of a quantum channel are proved, necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these…
In this paper, we prove that assuming the exponential time hypothesis (ETH), there is no $f(k)\cdot n^{k^{o(1/\log\log k)}}$-time algorithm that can decide whether an $n$-vertex graph contains a clique of size $k$ or contains no clique of…
We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…
The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…
Motivated by deterministic identification via classical channels, where the encoder is not allowed to use randomization, we revisit the problem of identification via quantum channels but now with the additional restriction that the message…
Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and well understood when the channel is accurately modelled by classical physics. However, when quantum effects…
The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given $n$ points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and…
This paper studies the zero error capacity of the Nearest Neighbor Error (NNE) channels with a multilevel alphabet. In the NNE channels, a transmitted symbol is a $d$-tuple of elements in $\{0,1,2,\dots, n-1 \}$. It is assumed that only one…
We define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a…
We present a new way of encoding a quantum computation into a 3-local Hamiltonian. Our construction is novel in that it does not include any terms that induce legal-illegal clock transitions. Therefore, the weights of the terms in the…
The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords.…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum…
Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the…
Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage,…