Related papers: Complexity and capacity bounds for quantum channel…
The complexity of a quantum gate, defined as the minimal number of elementary gates to build it, is an important concept in quantum information and computation. It is shown recently that the complexity of quantum gates built from random…
We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of…
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
In this work we aim at quantifying quantum channel output similarity. In order to achieve this, we introduce the notion of quantum channel superfidelity, which gives us an upper bound on the quantum channel fidelity. This quantity is…
A crucial step towards the 6th generation (6G) of networks would be a shift in communication paradigm beyond the limits of Shannon's theory. In both classical and quantum Shannon's information theory, communication channels are generally…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions ---many examples of which have…
In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set $\Theta(2^{n})$ bits with respect to classical…
We initiate the study of zero-error communication via quantum channels when the receiver and sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
The entanglement-assisted classical capacity of a quantum channel is known to provide the formal quantum generalization of Shannon's classical channel capacity theorem, in the sense that it admits a single-letter characterization in terms…
We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private…
Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication…
Noisy quantum channels may be used in many information carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on…
We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
Recently the power of positive partial transpose preserving (PPTp) and no-signalling (NS) codes in quantum communication has been studied. We continue with this line of research and show that the NS/PPTp/NS$\cap$PPTp codes assisted…
We show that approximating the trace norm contraction coefficient of a quantum channel within a constant factor is NP-hard. Equivalently, this shows that determining the optimal success probability for encoding a bit in a quantum system…
We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are…
We consider a notion of complexity of quantum channels in relativistic continuum quantum field theory (QFT) defined by the distance to the trivial (identity) channel. Our distance measure is based on a specific divergence between quantum…