Security of the Bennett 1992 quantum-key distribution against individual attack over a realistic channel

The security of two-state quantum key distribution against individual attack is estimated when the channel has losses and noises. We assume that Alice and Bob use two nonorthogonal single-photon polarization states. To make our analysis simple, we propose a modified B92 protocol in which Alice and Bob make use of inconclusive results and Bob performs a kind of symmetrization of received states. Using this protocol, Alice and Bob can estimate Eve's information gain as a function of a few parameters which reflect the imperfections of devices or Eve's disturbance. In some parameter regions, Eve's maximum information gain shows counter-intuitive behavior, namely, it decreases as the amount of disturbances increases. For a small noise rate Eve can extract perfect information in the case where the angle between Alice's two states is small or large, while she cannot extract perfect information for intermediate angles. We also estimate the secret key gain which is the net growth of the secret key per one pulse. We show the region where the modified B92 protocol over a realistic channel is secure against individual attack.Comment: 16 pages, 15 figure

Existence of perfect Mendelsohn designs with k=5 and λ>1

AbstractLet υ, k, and λ be positive integers. A (υ, k, λ)-Mendelsohn design (briefly (υ, k, λ)-MD) is a pair (X, B) where X is a υ-set (of points) and B is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X are consecutive in exactly λ blocks of B. A set of k distinct elements {a1, a2,…, ak} is said to be cyclically ordered by a1<a2<⋯<ak<a1 and the pair ai, ai+t is said to be t-apart in cyclic k-tuple (a1, a2,…, ak) where i+t is taken modulo k. It for all t=1,2,…, k-1, every ordered pair of points of X is t-apart in exactly λ blocks of B, then the (υ, k, λ)-MD is called a perfect design and is denoted briefly by (υ, k, λ)-PMD. In this paper, we shall be concerned mainly with the case where k=5 and λ>1. It will be shown that the necessary condition for the existence of a (υ, 5, λ)-PMD, namely, λv(υ-1)≡0 (mod 5), is also sufficient for λ>1 with the possible exception of pairs (υ, λ) where λ=5 and υ=18 and 28

Quantum copying: Fundamental inequalities

How well one can copy an arbitrary qubit? To answer this question we consider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they are not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bound for the amount of noise induced by quantum copying. We examine both copying transformations which produce one copy and transformations which produce many, and show that the quality of each copy decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.

Robustness of quantum Markov chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.Comment: 14 pages, no figures; not for the feeble-minde

Creating Bell states and decoherence effects in quantum dots system

We show how to improve the efficiency for preparing Bell states in coupled two quantum dots system. A measurement to the state of driven quantum laser field leads to wave function collapse. This results in highly efficiency preparation of Bell states. The effect of decoherence on the efficiency of generating Bell states is also discussed in this paper. The results show that the decoherence does not affect the relative weight of $|00>$ and $|11>$ in the output state, but the efficiency of finding Bell states.Comment: 4 pages, 2figures, corrected some typo

Maximizing the entanglement of two mixed qubits

Two-qubit states occupy a large and relatively unexplored Hilbert space. Such states can be succinctly characterized by their degree of entanglement and purity. In this letter we investigate entangled mixed states and present a class of states that have the maximum amount of entanglement for a given linear entropy.Comment: 4 pages, 3 figure

Quantum state merging and negative information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.Comment: 23 pages, 3 figure

Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticise this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch's condition when mixed states are treated as representing an observer's knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.Comment: 10 pages, 6 figures, comments welcome; v2 added references and clarified some points; v3 published versio

Retrodiction of Generalised Measurement Outcomes

If a generalised measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalised measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement (where each POVM element corresponds to a single Kraus operator) for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realised in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalised measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are non-singular. From this, we deduce that every trace-preserving quantum operation is associated with a generalised measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review

Black holes as mirrors: quantum information in random subsystems

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.Comment: 18 pages, 2 figures. (v2): discussion of decoding complexity clarifie