There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on an eavesdropper's power. This article provides a concise up-to-date review of QKD, biased toward the practical side. Essential theoretical tools that have been developed to assess the security of the main experimental platforms are presented (discrete-variable, continuous-variable, and distributed-phase-reference protocols).

/pdf/the-security-of-practical-quantum-key-distribution-1qnjoq3c7p.pdf

The security of practical quantum key distribution

The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

/pdf/gaussian-quantum-information-3ac4tfs0tm.pdf

Gaussian quantum information

We present the optimal collective attack on a quantum key distribution protocol in the "device-independent" security scenario, where no assumptions are made about the way the quantum key distribution devices work or on what quantum system they operate. Our main result is a tight bound on the Holevo information between one of the authorized parties and the eavesdropper, as a function of the amount of violation of a Bell-type inequality.

/pdf/device-independent-security-of-quantum-cryptography-against-18at9y8j95.pdf

Device-independent security of quantum cryptography against collective attacks.

A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities

The private classical capacity and quantum capacity of a quantum channel

We study and solve the problem of distilling a secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via oneway public discussion: we...

Distillation of secret key and entanglement from quantum states

An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel. Although our formula involves regularization, i.e. taking a limit over many copies of the channel, it reduces to a single-letter expression in the case of generalized dephasing channels. Analogous formulas are conjectured for the simultaneous public-private capacity of a quantum channel and for the simultaneously 1-way distillable common randomness and entanglement of a bipartite quantum state.

The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information

We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error-correcting codes, thus allowing us to "quantize" all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.

https://arxiv.org/pdf/quant-ph/0610092.pdf

Correcting quantum errors with entanglement.

We give a simple, direct proof of the ‘mother’ protocol of quantum information theory. In this new formulation, it is easy to see that the mother, or rather her generalization to the fully quantum Slepian–Wolf protocol, simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation and state transfer from the sender to the receiver. As a result, in addition to her other ‘children’, the mother protocol generates the state-merging primitive of Horodecki, Oppenheim and Winter, a fully quantum reverse Shannon theorem, and a new class of distributed compression protocols for correlated quantum sources which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called ‘father’ protocol whose children provide the quantum capacity and the entanglement-assisted capacity of a quantum channel, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.

/pdf/the-mother-of-all-protocols-restructuring-quantum-1y8494bcdv.pdf

Igor Devetak

Papers

The private classical capacity and quantum capacity of a quantum channel

Distillation of secret key and entanglement from quantum states

The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information

Correcting quantum errors with entanglement.

The mother of all protocols: restructuring quantum information’s family tree