Titles and Abstracts

Speaker:

Mario Berta

Title:

Single-Shot Quantum State Merging

Abstract:

We consider an unknown quantum state shared between two parties, Alice and Bob, and ask how much quantum communication is needed to transer the full state to Bob. This problem is known as state merging and was introduced in [Horodecki et al., Nature, 436, 673 (2005)]. It has been shown that for free classical communication the minimal number of quantum bits that need to be sent from Alice to Bob is given by the conditional von Neumann entropy. However this result only holds asymptotically (in the sense that Alice and Bob share initially many identical copies of the state) and it was unclear how much quantum communication is necessary to merge a single copy. We show that the minimal amount of quantum communication needed to achieve this single-shot state merging is given by minus the smooth conditional min-entropy of Alice conditioned on the environment. This gives an operational meaning to the smooth conditional min-entropy.

Speaker:

Giulio Chiribella

Title:

Dilation of physical processes in general probabilistic theories (PDF)

Abstract:

Dilation theorems, such as Stinespring's dilation of quantum operations and Ozawa's dilation of quantum instruments, represent a fundamental structure of quantum mechanics and are extremely rich of consequences in quantum information theory. In the general probabilistic framework it is natural to search for the characterization of probabilistic theories that, similarly to quantum mechanics, allow for such a dilation of physical processes. In this work we prove the equivalence between process-dilation and the purification of mixed states, showing that the purification of ensembles of mixed states entails the existence of a "Choi-Jamiolkowski" isomorphism between transformations and bipartite states, and allows one to implement teleportation in a deterministic fashion. Moreover, as a consequence of the general dilation theorem, multipartite channels satisfying causal conditions can be characterized as those resulting from the sequential concatenation of channels with memory, thus extending the known result about quantum memory channels to the general probabilistic framework.

Speaker:

Roger Colbeck

Title:

Simple Channel Coding Bounds

Abstract:

I will show how classical one-shot channel coding bounds become very simple to derive if looked at in terms of smooth Renyi divergences. The simplicity of the proof strongly indicates that these quantities really are the right measures (at least for this task). I will compare these bounds with existing ones. This is based on work with Ligong Wang and Renato Renner.

Speaker:

Giacomo Mauro D'Ariano

Title:

Seeking a principle of quantumness

Abstract:

Quantum Mechanics is a beautiful simple mathematical structure---Hilbert spaces and operator algebras---with an unprecedented predicting power in the whole physical domain. However, after more than centrury from its birth, we still don't have a "principle" from which to derive the mathematical framework. The situation is similar to that of Lorentz transformations before the advent of the relativity principle. The relativity principle, along with the existence of a limiting velocity, are not just physical principles: they are mandatory operational principles without which one cannot guarantee local knowability and controllability in an experiment.

The large part of the formal structure of QM is a set of formal tools for describing the process of gathering information in any experiment, independently on the particular physics involved. It is mainly a kind of "information theory", a theory about our knowledge of physical entities rather than about the entities themselves. If we strip off such informational part from the theory, what would be left should be a "principle of the quantumness" from which QM should be derived.

In my talk I will show how two operational principles: NSF---"no-signaling from the future" (for the possibility of making predictions on the basis of past tests), and PFAITH---"the existence of a pure faithful state" (for the possibility of preparing any state and calibrating any test) restrict the set of possible probabilistic theories to a small set that includes quantum theory and excludes the classical one. All theories satisfying NSF admit a C*-algebra representation of events as linear

transformations of effects, and are "no-signaling without interaction". Postulate PFAITH then implies the "local observability principle" and the tensor-product structure for the linear spaces of states and effects. It also implies a remarkable list of additional features that are typically quantum, such as purification for some states, impossibility of bit commitment, and many other. An additional principle of purifiability (PURIFY) of all states would lead also to the existence of a "unitary" dilation for all deterministic transformations (this will be the subject of the talk of Giulio Chiribella). Dual to Postulate PFAITH an analogous postulate for effects (FAITHE) would give additional quantum features, such as teleportation. However, all possible consequences of these postulates still need to be investigated, and it is not clear yet if we can derive QM from the present postulates only. In order to prove that the probabilistic theory is quantum, one needs to show that also the effects make a C*-algebra, which is equivalent to atomicity of evolution (AE) in conjunction with the Choi-Jamiolkowski isomorphism (CJ), thus identifying effects with atomic events.

In order to understand the role of various principles in selecting different probabilistic theories we need "toy theories" alternative to the quantum and the classical one. I will analyze an extended version of the theory of Popescu Rohrlich boxes (which includes also transformations) and a new toy probabilistic theory: the "two clocks".

Speaker:

Nicolas Dutil

Title:

Multi-Party State Merging

Abstract:

In this talk, we look at a more general version of state merging, where many spatially separated parties want to send their share of a state to a receiver (Bob). We give necessary and sufficient conditions for the protocol to work by LOCC in a scenario where many copies are available. We also extend the protocol to a situation where two receivers are available so that a subset of the senders can send their share to one receiver, and the complement of that subset will transmit to the other receiver. We end the talk by looking at conditions for multi-state merging using only a single copy of the input state (i.e single-shot scenario). In this talk, we look at a more general version of state merging, where many spatially separated parties want to send their share of a state to a receiver (Bob).

Speaker:

Jonathan Oppenheim

Title:

Mutual Independence

Abstract:

We introduce the concept of mutual independence—correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key—it is a fully quantum and more general form of privacy. The states which possess mutual independence also generalize the so called private states— those that possess private key. We then show that the problem of distributed compression of quantum information can be solved in terms of mutual independence. We suspect that mutual independence is a highly singular quantity, i.e. that it is positive only on a set of measure zero; furthermore, we believe that its presence is seen on the single copy level. This appears to be born out in the classical case.

Speaker:

Paolo Perinotti

Title:

Quantum Combs for Learning, Computing and Cryptography (PDF)

Abstract:

We present some application of the recent theory of quantum combs [Phys. Rev. Lett. 101, 060401 (2008)] to information theoretic tasks. Quantum combs are exploited here for three main purposes. The first purpose is to optimise the quantum network for storage and retrieval of unitary gates. The quantum network accepts a finite number of black boxes performing a unitary transformation in a first stage, as a training set of examples, and learns from them to perform the transformation on new states, that will be available in a second stage. The second application is quantum computation. We introduce the particular combs used for quantum network estimation, named testers, and their application to unitary channel estimation and discrimination, showing how all the main quantum algorithms for computation are testers for the discrimination of classes of quantum oracle gates. Optimisation of unitary channel discrimination is then equivalent to optimisation of quantum algorithms. The third application of combs is the design of cryptographic and game theoretical interactive protocols. We show how this way of representing protocols allows for a simplified proof of impossibility of quantum bit commitment.

Speaker:

Renato Renner

Title:

Smooth Entropies

Abstract:

The information-theoretic treatment of correlated or finite resources naturally leads to a generalization of the notion of von Neumann entropy. More precisely, the von Neumann entropy "splits" into two distinct entropic quantities, called smooth min- and max-entropy, which can be seen as the two opposite ends of the spectrum of Renyi entropies.

In this talk, I will motivate and explain the notion of smooth min- and max-entropies. A focus will be on a duality relation between them, which allows to reduce their treatment to one single entropic quantity. I will review some remarkable consequences of this duality and illustrate them with examples, in particular in the context of state merging.

Speaker:

Marco Tomamichel

Title:

A Fully Quantum Asymptotic Equipartition Property

Abstract:

The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. In this paper, we prove a fully quantum generalization of this property, where both the output of the experiment and side information are quantum. We give an explicit bound on the convergence, which is independent of the dimensionality of the side information. This naturally leads to a family of Renyi-like quantum conditional entropies, for which the von Neumann entropy emerges as a special case.

Speaker:

Shashank Virmani

Title:

Many body physics and the capacity of quantum channels with memory

Abstract:

Motivated by suggestions that the capacity of correlated error quantum channels can display some interesting non-analytic behaviour, I will discuss work we have done looking at channels with memory that result from a many-body environment - with the aim of showing that critical behaviour (i.e. phase transitions) in the environment may be reflected in the capacity in some situations. We can construct some toy models where this can be shown to be the case, and we hope that as ultimately all correlations will be due to some underlying quantum field, that channels with a many-body 'flavour' should also be reasonably physical. Our hope is that with improvements in techniques such connections might be made more robust. The work has been done together with Martin Plenio, New Journal of Physics 10 (2008) 043032.

Speakers:

Francesco Buscemi & Nilanjana Datta

Title:

Towards a finite theory of entanglement (PDF)

Abstract:

Two relative entropic quantities are introduced, which act as parent quantities for optimal one-shot rates of various protocols in quantum information theory. These relative entropies have interesting operational interpretations in state discrimination. Further they give rise to new entanglement monotones which can be interpreted as optimal one-shot rates of entanglement manipulation under non-entangling maps and LOCC.