75 research outputs found
Quantum money with nearly optimal error tolerance
We present a family of quantum money schemes with classical verification
which display a number of benefits over previous proposals. Our schemes are
based on hidden matching quantum retrieval games and they tolerate noise up to
23%, which we conjecture reaches 25% asymptotically as the dimension of the
underlying hidden matching states is increased. Furthermore, we prove that 25%
is the maximum tolerable noise for a wide class of quantum money schemes with
classical verification, meaning our schemes are almost optimally noise
tolerant. We use methods in semi-definite programming to prove security in a
substantially different manner to previous proposals, leading to two main
advantages: first, coin verification involves only a constant number of states
(with respect to coin size), thereby allowing for smaller coins; second, the
re-usability of coins within our scheme grows linearly with the size of the
coin, which is known to be optimal. Lastly, we suggest methods by which the
coins in our protocol could be implemented using weak coherent states and
verified using existing experimental techniques, even in the presence of
detector inefficiencies.Comment: 17 pages, 5 figure
Quantum Communication Complexity with Coherent States and Linear Optics
We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming a wide class of protocols in quantum communication into a form in which they can be implemented with current technology. In particular, we apply the mapping to quantum communication complexity, providing general conditions under which quantum protocols can be implemented with coherent states and linear optics while retaining exponential separations in communication complexity compared to the classical case. Finally, we make use of our results to construct a protocol for the Hidden Matching problem that retains the known exponential gap between quantum and classical one-way communication complexity
Quantum superiority for verifying NP-complete problems with linear optics
Demonstrating quantum superiority for some computational task will be a
milestone for quantum technologies and would show that computational advantages
are possible not only with a universal quantum computer but with simpler
physical devices. Linear optics is such a simpler but powerful platform where
classically-hard information processing tasks, such as Boson Sampling, can be
in principle implemented. In this work, we study a fundamentally different type
of computational task to achieve quantum superiority using linear optics,
namely the task of verifying NP-complete problems. We focus on a protocol by
Aaronson et al. (2008) that uses quantum proofs for verification. We show that
the proof states can be implemented in terms of a single photon in an equal
superposition over many optical modes. Similarly, the tests can be performed
using linear-optical transformations consisting of a few operations: a global
permutation of all modes, simple interferometers acting on at most four modes,
and measurement using single-photon detectors. We also show that the protocol
can tolerate experimental imperfections.Comment: 10 pages, 6 figures, minor corrections, results unchange
Gaussian Boson Sampling using threshold detectors
We study what is arguably the most experimentally appealing Boson Sampling
architecture: Gaussian states sampled with threshold detectors. We show that in
this setting, the probability of observing a given outcome is related to a
matrix function that we name the Torontonian, which plays an analogous role to
the permanent or the Hafnian in other models. We also prove that, provided that
the probability of observing two or more photons in a single output mode is
sufficiently small, our model remains intractable to simulate classically under
standard complexity-theoretic conjectures. Finally, we leverage the
mathematical simplicity of the model to introduce a physically motivated, exact
sampling algorithm for all Boson Sampling models that employ Gaussian states
and threshold detectors.Comment: 5+5 pages, 2 figures. Closer to published versio
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