相关论文: Discretization of quantum pure states and local ra…

For large d, we study quantum channels on C^d obtained by selecting randomly N independent Kraus operators according to a probability measure mu on the unitary group U(d). When mu is the Haar measure, we show that for N>d/epsilon^2$, such a…

This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for $\epsilon$-randomizing maps, $n+2\log(1/\epsilon)+c$ bits required to $\epsilon$-randomize an…

Several techniques of generating random quantum channels, which act on the set of $d$-dimensional quantum states, are investigated. We present three approaches to the problem of sampling of quantum channels and show under which conditions…

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…

The random purification channel maps n copies of any mixed quantum state to n copies of a random purification of the state. We generalize this construction to arbitrary symmetries: for any group G of unitaries, we construct a quantum…

A random unitary channel is one that is given by a convex combination of unitary channels. It is shown that the conjectures on the additivity of the minimum output entropy and the multiplicativity of the maximum output $p$-norm can be…

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 the generation of quantum states and unitary operations that are ``random'' in certain respects. We show how to use such states to estimate the average fidelity, an important measure in the study of implementations of quantum…

We give a short proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to produce random codes by performing a unitarily covariant projective…

The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be…

Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or…

The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only near-perfect security is required, the size of the key…

We present a method to detect properties of quantum channels, assuming that some a priori information about the form of the channel is available. The method is based on a correspondence with entanglement detection methods for multipartite…

Channel-state duality is a central result in quantum information science. It refers to the correspondence between a dynamical process (quantum channel) and a static quantum state in an enlarged Hilbert space. Since the corresponding dual…

The concept of $\e$-randomizing quantum channels has been introduced by Hayden, Leung, Shor and Winter in connection with approximately encrypting quantum states. They proved using a discretization argument that sets of roughly $d \log d$…

We study the localization properties of bipartite channels, whose action on a subsystem yields a unitary channel. In particular we show that, under such channel, the subsystem must evolve independent of its environment. This point of view…

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…

The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in…

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the…

We show that a generic $N$-qudit pure quantum state is uniquely determined by only $2$ of its $\lceil\frac{N+1}{2}\rceil$-particle reduced density matrices. Therefore we give a method to uniquely determine a generic $N$-qudit pure state of…