This review introduces a new development in theoretical quantum physics, the ``resource-theoretic'' point of view. The approach aims to be closely linked to experiment, and to state exactly what result you can hope to achieve for what expenditure of effort in the laboratory. This development is an extension of the principles of thermodynamics to quantum problems; but there are resources that would never have been considered previously in thermodynamics, such as shared knowledge of a frame of reference. Many additional examples and new quantifications of resources are provided.

Quantum resource theories

Quantum cryptography is arguably the fastest growing area in quantum
information science. Novel theoretical protocols are designed on a regular
basis, security proofs are constantly improving, and experiments are
gradually moving from proof-of-principle lab demonstrations to in-field
implementations and technological prototypes. In this paper, we provide
both a general introduction and a state-of-the-art description of the
recent advances in the field, both theoretical and experimental. We start
by reviewing protocols of quantum key distribution based on discrete
variable systems. Next we consider aspects of device independence,
satellite challenges, and protocols based on continuous-variable systems.
We will then discuss the ultimate limits of point-to-point private
communications and how quantum repeaters and networks may overcome these
restrictions. Finally, we will discuss some aspects of quantum
cryptography beyond standard quantum key distribution, including quantum
random number generators and quantum digital signatures.

/pdf/advances-in-quantum-cryptography-47uxe1y6u2.pdf

Advances in quantum cryptography

Some years ago quantum hacking became popular: devices implementing the unbreakable quantum cryptography were shown to have imperfections which could be exploited by attackers. Security has been thoroughly enhanced, as a consequence of both theoretical and experimental advances. This review gives both sides of the story, with the current best theory of quantum security, and an extensive survey of what makes quantum cryptosystem safe in practice.

Secure quantum key distribution with realistic devices

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this review, we provide both a general introduction and a state of the art description of the recent advances in the field, both theoretically and experimentally. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum data locking and quantum digital signatures.

/pdf/advances-in-quantum-cryptography-2uyo6whymh.pdf

Advances in Quantum Cryptography

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schr\"odinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper the theory of quantum steering is reviewed. First, the basic concepts of steering and local hidden state models are presented and their relation to entanglement and Bell nonlocality is explained. Then various criteria for characterizing steerability and structural results on the phenomenon are described. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, applications of steering in quantum information processing and further related topics are reviewed.

Quantum Steering.

We study quantum channels that are close to another channel with weakly additive Holevo information, and we derive upper bounds on their classical capacity. Examples of channels with weakly additive Holevo information are entanglement-breaking channels, unital qubit channels, and Hadamard channels. Related to the method of approximate degradability, we define approximation parameters for each class above, which measure how close an arbitrary channel is to satisfying the respective property. This gives us upper bounds on the classical capacity in terms of functions of the approximation parameters, as well as an outer bound on the dynamic capacity region of a quantum channel. Since these parameters are defined in terms of the diamond distance, the upper bounds can be computed efficiently using semidefinite programming (SDP). We exhibit the usefulness of our method with two example channels: a convex mixture of amplitude damping and depolarizing noise and a composition of amplitude damping and dephasing noise. For both channels, our bounds perform well in certain regimes of the noise parameters in comparison to a recently derived SDP upper bound on the classical capacity. Along the way, we define the notion of a generalized channel divergence (which includes the diamond distance as an example), and we prove that for jointly covariant channels these quantities are maximized by purifications of a state invariant under the covariance group. This latter result may be of independent interest.

Approaches for approximate additivity of the Holevo information of quantum channels

This paper defines the amortized entanglement of a quantum channel as the largest difference in entanglement between the output and the input of the channel, where entanglement is quantified by an arbitrary entanglement measure. We prove that the amortized entanglement of a channel obeys several desirable properties, and we also consider special cases such as the amortized relative entropy of entanglement and the amortized Rains relative entropy. These latter quantities are shown to be single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of a quantum channel, respectively. Of especial interest is a uniform continuity bound for these latter two special cases of amortized entanglement, in which the deviation between the amortized entanglement of two channels is bounded from above by a simple function of the diamond norm of their difference and the output dimension of the channels. We then define approximately teleportation- and positive-partial-transpose-simulable (PPT-simulable) channels as those that are close in diamond norm to a channel which is either exactly teleportation- or PPT-simulable, respectively. These results then lead to single-letter upper bounds on the secret-key-agreement and PPT-assisted quantum capacities of channels that are approximately teleportation- or PPT-simulable, respectively. Finally, we generalize many of the concepts in the paper to the setting of general resource theories, defining the amortized resourcefulness of a channel and the notion of $\nu$-freely-simulable channels, connecting these concepts in an operational way as well.

https://iopscience.iop.org/article/10.1088/1751-8121/aa9da7/pdf

Amortized entanglement of a quantum channel and approximately teleportation-simulable channels

Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is evidence of having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., Phys. Rev. Lett. 119, 120503 (2017)] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement measure. As a consequence of this extension, we find tighter upper bounds on the nonasymptotic secret-key-agreement capacity of the lossy thermal bosonic channel than were previously known. The lossy thermal bosonic channel serves as a more realistic model of communication than the pure-loss bosonic channel, because it can model the effects of eavesdropper tampering and imperfect detectors. An implication of our result is that the previously known upper bounds on the secret-key-agreement capacity of the thermal channel are too pessimistic for the practical finite-size regime in which the channel is used a finite number of times, and so it should now be somewhat easier to witness a working quantum repeater when using secret-key-agreement capacity upper bounds as a benchmark.

Upper bounds on secret-key agreement over lossy thermal bosonic channels

It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807–3820, 2009. 
arXiv:0804.0686

) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein’s lemma for classical–quantum channels by showing that asymptotically the exponential error rate for classical–quantum channel discrimination is not improved by adaptive strategies. Second, we recover many other classes of channels for which adaptive strategies do not lead to an asymptotic advantage. Third, we give various converse bounds on the power of adaptive protocols for general asymptotic quantum channel discrimination. Intriguingly, it remains open whether adaptive protocols can improve the exponential error rate for quantum channel discrimination in the asymmetric Stein setting. Our proofs are based on the concept of amortized distinguishability of quantum channels, which we analyse using data-processing inequalities.

Amortized channel divergence for asymptotic quantum channel discrimination

In this paper, we introduce intrinsic non-locality as a quantifier for Bell non-locality, and we prove that it satisfies certain desirable properties such as faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation $p$. We also prove that intrinsic steerability is an upper bound on the secret-key-agreement capacity of any semi-device-independent protocol conducted using a device characterized by an assemblage $\hat{\rho}$. We also establish the faithfulness of intrinsic steerability and intrinsic non-locality. Finally, we prove that intrinsic non-locality is bounded from above by intrinsic steerability.

https://iopscience.iop.org/article/10.1088/1367-2630/ab6eaa/pdf

Eneet Kaur

Papers

Approaches for approximate additivity of the Holevo information of quantum channels

Amortized entanglement of a quantum channel and approximately teleportation-simulable channels

Upper bounds on secret-key agreement over lossy thermal bosonic channels

Amortized channel divergence for asymptotic quantum channel discrimination

Fundamental limits on key rates in device-independent quantum key distribution