arXiv subjects

Janos Bergou

Publications and source records attributed to Janos Bergou.

6 recordsLinked to original sources

arXiv2013

Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination

We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it, and then on to Charlie, who also measures it. The object in both cases is to determine which state Alice sent. In an unambiguous state discrimination measurement, we never make a mistake, i.e. misidentify the state, but the measurement may fail, in which case we gain no information about which state was sent. We find that there is a nonzero probability for both Bob and Charlie to identify the state, and we maximize this probability. The probability that Charlie's measurement succeeds depends on how much information about the state Alice sent is left in the qubit after Bob's measurement, and this information can be quantified by the overlap between the two possible states in which Bob's measurement leaves the qubit. This paper is a first step toward developing a theory of nondestructive sequential quantum measurements, which could be useful in quantum communication schemes.

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arXiv2005

A universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states

We construct a device that can unambiguously discriminate between two unknown quantum states. The unknown states are provided as inputs, or programs, for the program registers and a third system, which is guaranteed to be prepared in one of the states stored in the program registers, is fed into the data register of the device. The device will then, with some probability of success, tell us whether the unknown state in the data register matches the state stored in the first or the second program register. We show that the optimal device, i. e. the one that maximizes the probability of success, is universal. It does not depend on the actual unknown states that we wish to discriminate.

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arXiv2005

Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination

Deterministic discrimination of nonorthogonal states is forbidden by quantum measurement theory. However, if we do not want to succeed all the time, i.e. allow for inconclusive outcomes to occur, then unambiguous discrimination becomes possible with a certain probability of success. A variant of the problem is set discrimination: the states are grouped in sets and we want to determine to which particular set a given pure input state belongs. We consider here the simplest case, termed quantum state filtering, when the $N$ given non-orthogonal states, $\{|ψ_{1} >,..., |ψ_{N} > \}$, are divided into two sets and the first set consists of one state only while the second consists of all of the remaining states. We present the derivation of the optimal measurement strategy, in terms of a generalized measurement (POVM), to distinguish $|ψ_1>$ from the set $\{|ψ_2 >,...,|ψ_N > \}$ and the corresponding optimal success and failure probabilities. The results, but not the complete derivation, were presented previously [\prl {\bf 90}, 257901 (2003)] as the emphasis there was on appplication of the results to novel probabilistic quantum algorithms. We also show that the problem is equivalent to the discrimination of a pure state and an arbitrary mixed state.

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arXiv2003

Quantum walks based on an interferometric analogy

There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the particle will move. The continuous walk operates with continuous time. Here a third model for a quantum walk is proposed, which is based on an analogy to optical interferometers. It is a discrete-time model, and the unitary operator that advances the walk one step depends only on the local structure of the graph on which the walk is taking place. No quantum coin is introduced. This type of walk allows us to introduce elements, such as phase shifters, that have no counterpart in classical random walks. Walks on the line and cycle are discussed in some detail, and a probability current for these walks is introduced. The relation to the coined quantum walk is also discussed. The paper concludes by showing how to define these walks for a general graph.

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arXiv2002

Quantitative conditional quantum erasure in two-atom resonance fluorescence

We present a conditional quantum eraser which erases the a priori knowledge or the predictability of the path a photon takes in a Young-type double-slit experiment with two fluorescent four-level atoms. This erasure violates a recently derived erasure relation which must be satisfied for a conventional, unconditional quantum eraser that aims to find an optimal sorting of the system into subensembles with particularly large fringe visibilities. The conditional quantum eraser employs an interaction-free, partial which-way measurement which not only sorts the system into optimal subsystems with large visibility but also selects the appropriate subsystem with the maximum possible visibility. We explain how the erasure relation can be violated under these circumstances.

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arXiv2000

Optimum unambiguous discrimination among linearly-independent non-orthogonal quantum states and its optical realization

The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without error. Such nonunitary transformations can be performed conditionally on quantum systems; a unitary transformation is carried out on a larger system of which the system of interest is a subsytem, a measurement is performed, and if the proper result is obtained, the desired nonunitary transformation will have been performed on the subsystem. We show how to construct generalized interferometers (multiports), which when combined with measurements on some of the output ports, implement nonunitary transformations of this type. The input states are single-photon states in which the photon is divided among several modes. A number of explicit examples of distinguishing among three nonorthogonal states are discussed, and the networks that optimally distinguish among these states are presented.

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