Achievable rates for the Gaussian quantum channel

Harrington, Jim; Preskill, John

doi:10.1103/physreva.64.062301

Cited by 81 publications

(102 citation statements)

References 28 publications

Supporting

Mentioning

101

Contrasting

Order By: Relevance

“…The matrixh(δ) gets finally transformed to the form 8) which is upper triangular with non-vanishing diagonal entries, and thus has 'full rank'. We may thus conclude that the coefficient matrix h(δ) is invertible, showing that the set…”

Section: The Amplifier Channel C2(κ)mentioning

confidence: 99%

“…The feasibility of processing information using Gaussian channels was originally explored in [1,7]. More recently, the problem of evaluating the classical capacity of Gaussian channels was addressed in [8][9][10], and the quantum capacities in [11][12][13][14][15][16]. In particular, the classical capacity of the attenuator channel was evaluated in [10], and the quantum capacity of a class of channels was studied in [12].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Operator-sum representation for bosonic Gaussian channels

2011

View full text Add to dashboard Cite

Operator-sum or Kraus representations for single-mode Bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can be simply read off from the matrix elements of a corresponding metaplectic operator. Kraus operators are employed to bring out, in the Fock basis, the manner in which the antilinear, unphysical matrix transposition map when accompanied by injection of a threshold classical noise becomes a physical channel, denoted D(κ) in the Holevo classification. The matrix transposition channels D(κ), D(κ −1 ) turn out to be a dual pair in the sense that their Kraus operators are related by the adjoint operation. The amplifier channel with amplification factor κ and the beamsplitter channel with attenuation factor κ −1 turn out to be mutually dual in the same sense. The action of the quantum-limited attenuator and amplifier channels as simply scaling maps on suitable quasiprobabilities in phase space is examined in the Kraus picture. Consideration of cumulants is used to examine the issue of fixed points. The semigroup property of the amplifier and attenuator families leads in both cases to a Zeno-like effect arising as a consequence of interrupted evolution. In the cases of entanglement-breaking channels a description in terms of rank one Kraus operators is shown to emerge quite simply. In contradistinction, it is shown that there is not even one finite rank operator in the entire linear span of Kraus operators of the quantum-limited amplifier or attenuator families, an assertion far stronger than the statement that these are not entanglement breaking channels. A characterization of extremality in terms of Kraus operators, originally due to Choi, is employed to show that all quantum-limited Gaussian channels are extremal. The fact that every noisy Gaussian channel can be realised as product of a pair of quantum-limited channels is used to construct a discrete set of linearly independent Kraus operators for noisy Gaussian channels, including the classical noise channel, and these Kraus operators have a particularly simple structure.

show abstract

Section: The Amplifier Channel C2(κ)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Operator-sum representation for bosonic Gaussian channels

2011

View full text Add to dashboard Cite

show abstract

“…One can generalize the Shor and Preskill security proof to quNits [25]. In a recent result due to Harrington and Preskill, an achievable rate for quNit CSS codes is estimated in [26] (equation (76)). It is given by…”

Section: Finite Coherent Eavesdropping Attacksmentioning

confidence: 99%

Quantum key distribution using multilevel encoding: security analysis

Bourennane¹,

Björk²,

Gisin³

et al. 2002

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N-dimensional Hilbert space. We estimate both the mutual information between the legitimate parties and the eavesdropper, and the error rate, as a function of the dimension of the Hilbert space. We derive the information gained by an eavesdropper using optimal incoherent attacks and an upper bound on the legitimate party error rate that ensures unconditional security when the eavesdropper uses finite coherent eavesdropping attacks. We also consider realistic systems where we assume that the detector dark count probability is not negligible.

show abstract

“…He discussed it in the context of preservation of quantum states, which are to be used for quantum computation in the presence of quantum noise. There is a known upper bound on the quantum capacity based on the quantity called coherent information, and some authors conjecture that this bound is tight [2], [3, Section VI], [4], [5], [6]. On the other hand, known lower bounds appear to have left much room for improvement.…”

Section: Introductionmentioning

confidence: 99%

“…Good surveys on these problems have been given in [3] and [5]. An incomplete list of contributions after either of these surveys includes [23], [6], [4], [24], [25], [26], [27], [28], [29], [30], [31], [32]. Especially, we have witnessed the determination of the entanglement-assisted capacity [30] (see also [31]) and the settlement of the additivity problem of the classical capacity for several classes of channels [26], [27], [29] while these are not the capacity which this paper will be concerned with.…”

Section: Introductionmentioning

confidence: 99%

Information Rates Achievable With Algebraic Codes on Quantum Discrete Memoryless Channels

Hamada

2005

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, this work's bound is actually the highest possible rate at which symplectic stabilizer codes work reliably. KeywordsCompletely positive (CP) linear maps, fidelity, symplectic geometry, the method of types, quantum capacity, quantum error-correcting codes.

show abstract

Achievable rates for the Gaussian quantum channel

Cited by 81 publications

References 28 publications

Operator-sum representation for bosonic Gaussian channels

Operator-sum representation for bosonic Gaussian channels

Quantum key distribution using multilevel encoding: security analysis

Information Rates Achievable With Algebraic Codes on Quantum Discrete Memoryless Channels

Contact Info

Product

Resources

About