Hello,
Tomorrow Tuesday, we will have two seminar talks, by Fernando Brandao and by Niek Bouman. We therefore start already at 16:30. Both talks will be on Hoenggerberg.
Best regards, Stefan
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Tuesday, March 15, 16:30 - 18:00, HIT J 51.
Fernando Brandao:
"The quantum one-time pad and superactivation"
A classical one-time pad allows two parties to send private messages over a public classical channel -- an eavesdropper who intercepts the communication learns nothing about the message. In this talk I will discuss a quantum analogue of this task: two parties initially share a quantum state and use an insecure quantum channel to communicate privately. I will show that the optimal rate is given by an additive and single-letter expression, a direct quantum analogue of the celebrated classical formula. The rate turns out to be equal to the quantum capacity assisted by symmetric side-channels, a quantity which had a key role in showing superactivation of the quantum capacity, but which lacked a clear operational meaning. In this way, the symmetric side-channel receives an interpretation as a quantum public channel. I will also discuss how taking this relation further gives new insight into superactivation of the channel capacity by showing the equivalence of (noisy) quantum privacy and distillable entanglement under public quantum communication. This is based on joint work with Jonathan Oppenheim (arXiv:1004.3328, arXiv:1005.1975)
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Niek Bouman:
"Sampling in a Quantum Population"
Random sampling can be used to estimate a property from a population by merely looking at some randomly selected elements of that population. Classically, this is very well understood and useful tools (such as exponential-tail bounds on the accuracy of the estimate) are available. For example, the relative Hamming weight of a bit string (the fraction of non-zero positions in the string) can be estimated by determining the relative Hamming weight of a random subset of the bits.
Suppose that we apply random sampling to a multi-qubit quantum system: we select some qubit positions at random and measure these qubits in some reference basis. Now, the main question is: What can we conclude, given this measurement outcome, about the remaining part of the quantum state?
In this talk, we present our solution to this question, and formalize the intuition that the random sample should contain some information about the remaining qubits. As a corollary to our results, we get a lower-bound on the min-entropy (conditioned on an auxiliary quantum system that could be entangled to the qubits) of the outcomes obtained when measuring the remaining qubits in some specific basis.
As part of our "framework", we define a "quantum error probability", which is, informally speaking, the probability that our conclusions about the remaining qubits, drawn based on the sample, are incorrect. We furthermore show that an upper bound on this quantum error probability can be easily computed from the error probability of the corresponding classical sampling procedure (by which we mean the same sampling distribution and method to compute the estimate, but then applied to a classical population). As a consequence of this, it suffices to analyze the classical sampling procedure, which is much easier.
We also demonstrate that our techniques are useful as a proof technique for BB84 quantum key distribution and quantum oblivious transfer. Both protocols contain a "checking phase" where a random subset of the qubits is selected and measured. Then, in both cases, the min-entropy bound on future measurement outcomes that follows from these sample measurements almost directly leads to a security proof.
See also http://arxiv.org/abs/0907.4246
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