Entangling capacity of global phases and implications for Deutsch-Jozsa algorithm

We investigate the creation of entanglement by the application of phases whose value depends on the state of a collection of qubits. First we give the necessary and sufficient conditions for a given set of phases to result in the creation of entanglement in a state comprising of an arbitrary number of qubits. Then we analyze the creation of entanglement between any two qubits in three qubit pure and mixed states. We use our result to prove that entanglement is necessary for Deutsch-Jozsa algorithm to have an exponential advantage over its classical counterpart.Comment: All 8 figures at the en

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

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

Conditional beam splitting attack on quantum key distribution

We present a novel attack on quantum key distribution based on the idea of adaptive absorption [calsam01]. The conditional beam splitting attack is shown to be much more efficient than the conventional beam spitting attack, achieving a performance similar to the, powerful but currently unfeasible, photon number splitting attack. The implementation of the conditional beam splitting attack, based solely on linear optical elements, is well within reach of current technology.Comment: Submitted to Phys. Rev.

On Bures fidelity of displaced squeezed thermal states

Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this paper, we give a formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters and birefly discuss how the results can apply to quantum information theory.Comment: 10 pages with RevTex require

Maximal entanglement of squeezed vacuum states via swapping with number-phase measurement

We propose a method to refine entanglement via swapping from a pair of squeezed vacuum states by performing the Bell measurement of number sum and phase difference. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe the teleportation of number states by using the entangled states prepared in this way.Comment: 4 pages, 1 PS figure, RevTe

Teleportation-based number state manipulation with number sum measurement

We examine various manipulations of photon number states which can be implemented by teleportation technique with number sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.Comment: 9 pages, 4 figures, Misprints are corrected. 3 figures for number sum measurement are added. Discussion on manipulations are expanded. Calculations for success probabilities are added. Fig.4 is adde

Teleportation of a Zero-and One-photon Running Wave State by Projection Synthesis

We show how to teleport a running wave superposition of zero- and one-photon field state through the projection synthesis technique. The fidelity of the scheme is computed taking into account the noise introduced by dissipation and the efficiency of the detectors. These error sources have been introduced through a single general relationship between input and output operators.Comment: 11 pages, 1 figur

Strong subadditivity inequality for quantum entropies and four-particle entanglement

Strong subadditivity inequality for a three-particle composite system is an important inequality in quantum information theory which can be studied via a four-particle entangled state. We use two three-level atoms in $\Lambda$ configuration interacting with a two-mode cavity and the Raman adiabatic passage technique for the production of the four-particle entangled state. Using this four-particle entanglement, we study for the first time various aspects of the strong subadditivity inequality.Comment: 5 pages, 3 figures, RevTeX4, submitted to PR