250,306 research outputs found
State Discrimination with Post-Measurement Information
We introduce a new state discrimination problem in which we are given
additional information about the state after the measurement, or more
generally, after a quantum memory bound applies. In particular, the following
special case plays an important role in quantum cryptographic protocols in the
bounded storage model: Given a string x encoded in an unknown basis chosen from
a set of mutually unbiased bases, you may perform any measurement, but then
store at most q qubits of quantum information. Later on, you learn which basis
was used. How well can you compute a function f(x) of x, given the initial
measurement outcome, the q qubits and the additional basis information? We
first show a lower bound on the success probability for any balanced function,
and any number of mutually unbiased bases, beating the naive strategy of simply
guessing the basis. We then show that for two bases, any Boolean function f(x)
can be computed perfectly if you are allowed to store just a single qubit,
independent of the number of possible input strings x. However, we show how to
construct three bases, such that you need to store all qubits in order to
compute f(x) perfectly. We then investigate how much advantage the additional
basis information can give for a Boolean function. To this end, we prove
optimal bounds for the success probability for the AND and the XOR function for
up to three mutually unbiased bases. Our result shows that the gap in success
probability can be maximal: without the basis information, you can never do
better than guessing the basis, but with this information, you can compute f(x)
perfectly. We also exhibit an example where the extra information does not give
any advantage at all.Comment: twentynine pages, no figures, equations galore. v2 thirtyone pages,
one new result w.r.t. v
Using post-measurement information in state discrimination
We consider a special form of state discrimination in which after the
measurement we are given additional information that may help us identify the
state. This task plays a central role in the analysis of quantum cryptographic
protocols in the noisy-storage model, where the identity of the state
corresponds to a certain bit string, and the additional information is
typically a choice of encoding that is initially unknown to the cheating party.
We first provide simple optimality conditions for measurements for any such
problem, and show upper and lower bounds on the success probability. For a
certain class of problems, we furthermore provide tight bounds on how useful
post-measurement information can be. In particular, we show that for this class
finding the optimal measurement for the task of state discrimination with
post-measurement information does in fact reduce to solving a different problem
of state discrimination without such information. However, we show that for the
corresponding classical state discrimination problems with post-measurement
information such a reduction is impossible, by relating the success probability
to the violation of Bell inequalities. This suggests the usefulness of
post-measurement information as another feature that distinguishes the
classical from a quantum world.Comment: 10 pages, 4 figures, revtex, v2: published version, minor change
Near optimal discrimination of binary coherent signals via atom-light interaction
We study the discrimination of weak coherent states of light with significant
overlaps by nondestructive measurements on the light states through measuring
atomic states that are entangled to the coherent states via dipole coupling. In
this way, the problem of measuring and discriminating coherent light states is
shifted to finding the appropriate atom-light interaction and atomic
measurements. We show that this scheme allows us to attain a probability of
error extremely close to the Helstrom bound, the ultimate quantum limit for
discriminating binary quantum states, through the simple Jaynes-Cummings
interaction between the field and ancilla with optimized light-atom coupling
and projective measurements on the atomic states. Moreover, since the
measurement is nondestructive on the light state, information that is not
detected by one measurement can be extracted from the post-measurement light
states through subsequent measurements.Comment: 11 pages, 9 figure
Sequential Discrimination Between Non-Orthogonal Quantum States
The problem of discriminating between non-orthogonal states is one that has generated a lot of interest. This basic formalism is useful in many areas of quantum information. It serves as a fundamental basis for many quantum key distribution schemes, it functions as an integral part of other quantum algorithms, and it is useful in experimental settings where orthogonal states are not always possible to generate. Additionally, the discrimination problem reveals important fundamental properties, and is intrinsically related to entanglement. In this thesis, the focus is on exploring the problem of sequentially discriminating between non-orthogonal states. In the simplest version these schemes, Alice sends one of two known pure states to Bob who performs a non-optimal discrimination procedure such that the post measurement states resulting from his measurement can then be discriminated by a third participant, Charlie. In these schemes, the goal is to optimize the joint probability of both Bob and Charlie succeeding. In devising such a scheme, there are several different criteria that can be prioritized. The most basic scheme, referred to as Minimum Error (ME) discrimination, prioritizes Bob\u27s and Charlie\u27s abilities to successfully determine which state was sent by Alice. In this scheme, Bob and Charlie each set up two detectors and based on the result from the detector they make a guess as to which state was sent. For instance, if Bob registers a click in his first detector, he concludes that Alice sent the first state. As each detector has some probability to produce a result for either incoming result, Bob and Charlie optimize their joint probability of success by optimizing the probability that each detector will fire when the correlated state is sent by Alice. Another possible scheme, referred to as Unambiguous Discrimination (UD), prioritizes Bob\u27s and Charlie\u27s ability to correctly determine the state sent by Alice. In this scheme, Bob and Charlie each set up three detectors, where if a result is obtained from the first two detectors Bob or Charlie can determine with certainty which state was sent by Alice. One final setup, referred to as Discrimination with a Fixed Rate of Inconclusive Outcome, is a combination of the previous two schemes, where Bob and Charlie maximize their probability of successfully determining the state sent by Alice where they allow some fixed probability that they will not be able to determine which state Alice sent. This fixed inconclusive probability allows Bob and Charlie to control how much they prioritize correctly determining the state that was sent, as in the Unambiguous Discrimination, versus prioritizing successfully determining the state sent by Alice, as in Minimum Error discrimination. One final topic that will be discussed by this thesis is Quantum Retrodiction. Quantum Retrodiction applies an alternate perspective on the communication protocol between Alice and Bob. In the predictive model, Alice calculates the probability that Bob gets a specific measurement result given that she prepares her system in a specific state. In the retrodictive model, Bob calculates the probability that Alice prepared her system in a specific state given the result of his measurement. This alternate perspective on the communication procedure gives new a new understanding and new tools for approaching the problem of state discrimination, as exemplified by applying the retrodictive formalism to unambiguous discrimination
Residual and Destroyed Accessible Information after Measurements
When quantum states are used to send classical information, the receiver
performs a measurement on the signal states. The amount of information
extracted is often not optimal due to the receiver's measurement scheme and
experimental apparatus. For quantum non-demolition measurements, there is
potentially some residual information in the post-measurement state, while part
of the information has been extracted and the rest is destroyed. Here, we
propose a framework to characterize a quantum measurement by how much
information it extracts and destroys, and how much information it leaves in the
residual post-measurement state. The concept is illustrated for several
receivers discriminating coherent states.Comment: 5 pages, 1 figur
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