Related papers: Hypercontractivity for Quantum Erasure Channels vi…
In classical information theory, the Doeblin coefficient of a classical channel provides an efficiently computable upper bound on the total-variation contraction coefficient of the channel, leading to what is known as a strong…
We introduce an infinite sequence of quantum channels for which the Holevo capacity is additive. The channel series is closely related to the quantum channels arising from universal quantum cloning machines. The additivity proof is…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the…
We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint…
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new…
A unified approach to prove the converses for the quantum channel capacity theorems is presented. These converses include the strong converse theorems for classical or quantum information transfer with error exponents and novel explicit…
We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with…
We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of commitment capacity for these channels and prove matching upper and lower bound on it in terms of the conditional entropy. Our…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly…
A quantum message is encoded into $N$ storage nodes (quantum systems $Q_1\dots Q_N$) with assistance from $N_B$ maximally entangled bi-partite quantum systems $A_1B_1, \dots, A_{N_B}B_{N_B}$, that are prepared in advance such that $B_1\dots…
In analogy with its classical counterpart, a noisy quantum channel is characterized by a loss, a quantity that depends on the channel input and the quantum operation performed by the channel. The loss reflects the transmission quality: if…
Entanglement shared between the two ends of a quantum communication channel has been shown to be a useful resource in increasing both the quantum and classical capacities for these channels. The entanglement-assisted capacities were derived…
We begin this thesis by expanding the technique of teleportation simulation, which adds noise to the entangled resource state to mimic channel effects. By introducing classical noise in the communication step, we show it is possible to…
Basing on recently developed convex programming framework in the paper [arXiv:2204.10626], we provide a proof for a long-standing conjecture on optimality of Gaussian encondings for the ultimate communication rate of generalized heterodyne…
We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have…
The two-way capacities of quantum channels determine the ultimate entanglement and secret-key distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since…
The Heisenberg limit provides a quadratic improvement over the standard quantum limit, and is the maximum quantum advantage that quantum sensors could provide over classical methods. This limit remains elusive, however, because of the…
Unextendibility of quantum states and channels is inextricably linked to the no-cloning theorem of quantum mechanics, it has played an important role in understanding and quantifying entanglement, and more recently it has found applications…