Fundamental rate-loss tradeoff for optical quantum key distribution

Takeoka, Masahiro; Guha, Saikat; Wilde, Mark M.

doi:10.1038/ncomms6235

Cited by 427 publications

(459 citation statements)

References 54 publications

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“…As far as applications are concerned, it is an open question if the von Neumann entropy based squashed entanglement is a strong converse rate for entanglement distillation; the Rényi squashed entanglement may be a useful tool in investigating this question. Also, using the Rényi squashed entanglement, one could try to prove that the von Neumann entropy based squashed entanglement is a strong converse rate for the two-way assisted quantum capacity of any channel (the weak converse bound being shown in [TGW14b,TGW14a] The fidelity of recovery quantifies how well one can recover the full state on systems ABC if system A is lost and one is allowed to perform a recovery map on system C alone. Thus, for states with small conditional mutual information (near to zero), the fidelity of recovery is high (near to one).…”

Section: Discussionmentioning

confidence: 99%

“…The squashed entanglement finds application as an upper bound on distillable entanglement and as a lower bound on entanglement cost [CW04]. The squashed entanglement of a quantum channel is defined as the maximum squashed entanglement that can be registered by a sender and a receiver at the input and output of a channel [TGW14b,TGW14a]. This quantity is an upper bound on the quantum communication capacity of any channel assisted by unlimited forward and backward classical communication as well as the private capacity of a quantum channel assisted by unlimited forward and backward public classical communication.…”

Section: Introductionmentioning

confidence: 99%

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Rényi squashed entanglement, discord, and relative entropy differences

Seshadreesan¹,

Berta²,

Wilde³

2015

J. Phys. A: Math. Theor.

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The squashed entanglement quantifies the amount of entanglement in a bipartite quantum state, and it satisfies all of the axioms desired for an entanglement measure. The quantum discord is a measure of quantum correlations that are different from those due to entanglement. What these two measures have in common is that they are both based upon the conditional quantum mutual information. In [Berta et al., J. Math. Phys. 56, 022205 (2015)], we recently proposed Rényi generalizations of the conditional quantum mutual information of a tripartite state on ABC (with C being the conditioning system), which were shown to satisfy some properties that hold for the original quantity, such as non-negativity, duality, and monotonicity with respect to local operations on the system B (with it being left open to show that the Rényi quantity is monotone with respect to local operations on system A). Here we define a Rényi squashed entanglement and a Rényi quantum discord based on a Rényi conditional quantum mutual information and investigate these quantities in detail. Taking as a conjecture that the Rényi conditional quantum mutual information is monotone with respect to local operations on both systems A and B, we prove that the Rényi squashed entanglement and the Rényi quantum discord satisfy many of the properties of the respective original von Neumann entropy based quantities. In our prior work [Berta et al., Phys. Rev. A 91, 022333 (2015)], we also detailed a procedure to obtain Rényi generalizations of any quantum information measure that is equal to a linear combination of von Neumann entropies with coefficients chosen from the set {−1, 0, 1}. Here, we extend this procedure to include differences of relative entropies. Using the extended procedure and a conjectured monotonicity of the Rényi generalizations in the Rényi parameter, we discuss potential remainder terms for well known inequalities such as monotonicity of the relative entropy, joint convexity of the relative entropy, and the Holevo bound.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rényi squashed entanglement, discord, and relative entropy differences

Seshadreesan¹,

Berta²,

Wilde³

2015

J. Phys. A: Math. Theor.

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“…A clear criterion for this is to surpass the TakeokaGuha-Wilde (TGW) bound [6,7]. This is an upper bound of the secret key rate per optical mode over a pure lossy channel, and given by R TGW = log 2 1 + η 1 − η ,…”

Section: Introductionmentioning

confidence: 99%

Role of syndrome information on a one-way quantum repeater using teleportation-based error correction

et al. 2016

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We investigate a quantum repeater scheme for quantum key distribution based on the work by Muralidharan et al., Phys. Rev. Lett. 112, 250501 (2014). Our scheme extends that work by making use of error syndrome measurement outcomes available at the repeater stations. We show how to calculate the secret key rates for the case of optimizing the syndrome information, while the known key rate is based on a scenario of coarse-graining the syndrome information. We show that these key rates can surpass the Pirandola-Laurenza-Ottaviani-Banchi bound on secret key rates of direct transmission over lossy bosonic channels.

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“…[34] and the upper bound of Ref. [35]. Furthermore, we know such repeater stations must include a non-Gaussian element [36].…”

Section: Resultsmentioning

confidence: 99%

Continuous-Variable Entanglement Swapping

Marshall

Weedbrook²

2015

Entropy

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We present a very brief overview of entanglement swapping as it relates to continuous-variable quantum information. The technical background required is discussed and the natural link to quantum teleportation is established before discussing the nature of Gaussian entanglement swapping. The limitations of Gaussian swapping are introduced, along with the general applications of swapping in the context of to quantum communication and entanglement distribution. In light of this, we briefly summarize a collection of entanglement swapping schemes which incorporate a non-Gaussian ingredient and the benefits of such schemes are noted. Finally, we motivate the need to further study and develop such schemes by highlighting requirements of a continuous-variable repeater.

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Fundamental rate-loss tradeoff for optical quantum key distribution

Cited by 427 publications

References 54 publications

Rényi squashed entanglement, discord, and relative entropy differences

Rényi squashed entanglement, discord, and relative entropy differences

Role of syndrome information on a one-way quantum repeater using teleportation-based error correction

Continuous-Variable Entanglement Swapping

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