Results 1  10
of
52
Additivity of the classical capacity of entanglementbreaking quantum channels
 J. Math. Phys
, 2002
"... We show that for the tensor product of an entanglementbreaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the HolevoSchumacherWestmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, ..."
Abstract

Cited by 59 (4 self)
 Add to MetaCart
(Show Context)
We show that for the tensor product of an entanglementbreaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the HolevoSchumacherWestmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [4, 12]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑
On Duality between Quantum Maps and Quantum States
, 2004
"... We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations, determined by unitary matrices of extended dimensionality, is defined and analyzed. Using the concept of the dynamical matrix and the Jamiolkowski isomorphism we explore the relation between the set of quantum operations (dynamics) and the set of density matrices acting on an extended Hilbert space (kinematics). An analogous relation is established between the classical maps and an extended space of the discrete probability distributions.
Relative entropy in quantum information theory
 CONTEMPORARY MATHEMATICS
, 2002
"... We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to quantify quantum entanglement and analyze its manipulation. ..."
Abstract

Cited by 23 (0 self)
 Add to MetaCart
We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to quantify quantum entanglement and analyze its manipulation.
HASTINGS’S ADDITIVITY COUNTEREXAMPLE VIA DVORETZKY’S THEOREM
"... Abstract. The goal of this note is to show that Hastings’s counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky’s theorem. ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
(Show Context)
Abstract. The goal of this note is to show that Hastings’s counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky’s theorem.
An efficient test for product states, with applications to quantum merlinarthur games
 In FOCS ’10: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science
, 2010
"... We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state ψ 〉 whose maximum overlap with a product state is 1 − ɛ, the test passes with probability 1 − Θ(ɛ), regardless of n or the local dimensions of the ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
(Show Context)
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state ψ 〉 whose maximum overlap with a product state is 1 − ɛ, the test passes with probability 1 − Θ(ɛ), regardless of n or the local dimensions of the individual systems. The test uses two copies of ψ〉. We prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarising channel. A key application of the test is to quantum MerlinArthur games, where we show that a witness from two unentangled provers can simulate a witness from arbitrarily many unentangled provers, up to a constant loss of soundness. Building on a previous result of Aaronson et al, this implies that there is an efficient quantum algorithm to verify 3SAT with constant soundness, given two unentangled proofs of Õ(√n) qubits. This result implies complexitytheoretic obstructions to finding a polynomialtime algorithm to determine separability of mixed quantum states, even up to constant error, and also to proving “weak ” variants of the additivity conjecture for quantum channels. Finally, our test can also be used to construct an efficient test for determining whether a unitary operator is a tensor product, which is a generalisation of classical linearity testing. 1
Quantum channels, wavelets, dilations and representations of On
 Proc. Edinb. Math. Soc
"... ar ..."
(Show Context)
Additivity of minimal entropy output for a class of covariant channels
"... channels ..."
(Show Context)
Classical capacity of a noiseless quantum channel assisted by noisy entanglement
, 2001
"... We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender’s share of the noisy entanglement plays the role of mut ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender’s share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.
Ruskai, “Multiplicativity properties of entrywise positive maps
, 2005
"... on matrix algebras ..."
(Show Context)
Nonadditivity of Rényi entropy and Dvoretzky’s theorem
 J. Math. Phys
, 2010
"... ar ..."
(Show Context)