Related papers: Approximate Private Quantum Channels
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…
This paper presents tight upper and lower bounds for minimum number of samples (copies of a quantum state) required to attain a prescribed accuracy (measured by error variance) for scalar parameters estimation using unbiased estimators…
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small…
We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter…
We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits…
Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact…
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…
We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…
We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of…
A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other…
Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
We study private quantum channels on a single qubit, which encrypt given set of plaintext states $P$. Specifically, we determine all achievable states $\rho^{(0)}$ (average output of encryption) and for each particular set $P$ we determine…
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…
Bosonic quantum communication has extensively been analysed in the asymptotic setting, assuming infinite channel uses and vanishing communication errors. Comparatively fewer detailed analyses are available in the non-asymptotic setting,…
Cryptographic protocols are often based on the two main resources: private randomness and private key. In this paper, we develop a relationship between these two resources. First, we show that any state containing perfect, directly…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…
It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn't asymptotically change. However, this is…
Given a correlation generated by a (possibly quantum) communication network, we study the amount of shared randomness required to generate it. We develop a novel upper bound for approximating distributions generated by arbitrary networks…