159 research outputs found
On the power quantum computation over real Hilbert spaces
We consider the power of various quantum complexity classes with the
restriction that states and operators are defined over a real, rather than
complex, Hilbert space. It is well know that a quantum circuit over the complex
numbers can be transformed into a quantum circuit over the real numbers with
the addition of a single qubit. This implies that BQP retains its power when
restricted to using states and operations over the reals. We show that the same
is true for QMA(k), QIP(k), QMIP, and QSZK.Comment: Significant improvements from previous version, in particular showing
both containments (eg. QMA_R is in QMA and vice versa
Generalized self-testing and the security of the 6-state protocol
Self-tested quantum information processing provides a means for doing useful
information processing with untrusted quantum apparatus. Previous work was
limited to performing computations and protocols in real Hilbert spaces, which
is not a serious obstacle if one is only interested in final measurement
statistics being correct (for example, getting the correct factors of a large
number after running Shor's factoring algorithm). This limitation was shown by
McKague et al. to be fundamental, since there is no way to experimentally
distinguish any quantum experiment from a special simulation using states and
operators with only real coefficients.
In this paper, we show that one can still do a meaningful self-test of
quantum apparatus with complex amplitudes. In particular, we define a family of
simulations of quantum experiments, based on complex conjugation, with two
interesting properties. First, we are able to define a self-test which may be
passed only by states and operators that are equivalent to simulations within
the family. This extends work of Mayers and Yao and Magniez et al. in
self-testing of quantum apparatus, and includes a complex measurement. Second,
any of the simulations in the family may be used to implement a secure 6-state
QKD protocol, which was previously not known to be implementable in a
self-tested framework.Comment: To appear in proceedings of TQC 201
Device independent state estimation based on Bell's inequalities
The only information available about an alleged source of entangled quantum
states is the amount by which the Clauser-Horne-Shimony-Holt (CHSH)
inequality is violated: nothing is known about the nature of the system or the
measurements that are performed. We discuss how the quality of the source can
be assessed in this black-box scenario, as compared to an ideal source that
would produce maximally entangled states (more precisely, any state for which
). To this end, we introduce several inequivalent notions of
fidelity, each one related to the use one can make of the source after having
assessed it; and we derive quantitative bounds for each of them in terms of the
violation . We also derive a lower bound on the entanglement of the source
as a function of only.Comment: 8 pages, 2 figures. Added appendices containing proof
Device independent quantum key distribution secure against coherent attacks with memoryless measurement devices
Device independent quantum key distribution aims to provide a higher degree
of security than traditional QKD schemes by reducing the number of assumptions
that need to be made about the physical devices used. The previous proof of
security by Pironio et al. applies only to collective attacks where the state
is identical and independent and the measurement devices operate identically
for each trial in the protocol. We extend this result to a more general class
of attacks where the state is arbitrary and the measurement devices have no
memory. We accomplish this by a reduction of arbitrary adversary strategies to
qubit strategies and a proof of security for qubit strategies based on the
previous proof by Pironio et al. and techniques adapted from Renner.Comment: 13 pages. Expanded main proofs with more detail, miscellaneous edits
for clarit
Alternative schemes for measurement-device-independent quantum key distribution
Practical schemes for measurement-device-independent quantum key distribution
using phase and path or time encoding are presented. In addition to immunity to
existing loopholes in detection systems, our setup employs simple encoding and
decoding modules without relying on polarization maintenance or optical
switches. Moreover, by employing a modified sifting technique to handle the
dead-time limitations in single-photon detectors, our scheme can be run with
only two single-photon detectors. With a phase-postselection technique, a
decoy-state variant of our scheme is also proposed, whose key generation rate
scales linearly with the channel transmittance.Comment: 30 pages, 5 figure
Efficient Heralding of Photonic Qubits with Apllications to Device Independent Quantum Key Distribution
We present an efficient way of heralding photonic qubit signals using linear
optics devices. First we show that one can obtain asymptotically perfect
heralding and unit success probability with growing resources. Second, we show
that even using finite resources, we can improve qualitatively and
quantitatively over earlier heralding results. In the latte r scenario, we can
obtain perfect heralded photonic qubits while maintaining a finite success
probability. We demonstrate the advantage of our heralding scheme by predicting
key rates for device independent quantum key distribution, taking imperfections
of sources and detectors into account
Determinism and Computational Power of Real Measurement-based Quantum Computation
International audienceMeasurement-based quantum computing (MBQC) is a universal model for quantum computation. The combinatorial characterisation of determinism in this model, powered by measurements, and hence, fundamentally probabilistic, is the cornerstone of most of the breakthrough results in this field. The most general known sufficient condition for a deterministic MBQC to be driven is that the underlying graph of the computation has a particular kind of flow called Pauli flow. The necessity of the Pauli flow was an open question. We show that the Pauli flow is necessary for real-MBQC, and not in general providing counterexamples for (complex) MBQC. We explore the consequences of this result for real MBQC and its applications. Real MBQC and more generally real quantum computing is known to be universal for quantum computing. Real MBQC has been used for interactive proofs by McKague. The two-prover case corresponds to real-MBQC on bipartite graphs. While (complex) MBQC on bipartite graphs are universal, the universality of real MBQC on bipartite graphs was an open question. We show that real bipartite MBQC is not universal proving that all measurements of real bipartite MBQC can be parallelised leading to constant depth computations. As a consequence, McKague techniques cannot lead to two-prover interactive proofs
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Orthographic facilitation in oral vocabulary acquisition
An experiment investigated whether exposure to orthography facilitates oral vocabulary learning. A total of 58 typically developing children aged 8-9 years were taught 12 nonwords. Children were trained to associate novel phonological forms with pictures of novel objects. Pictures were used as referents to represent novel word meanings. For half of the nonwords children were additionally exposed to orthography, although they were not alerted to its presence, nor were they instructed to use it. After this training phase a nonword-picture matching posttest was used to assess learning of nonword meaning, and a spelling posttest was used to assess learning of nonword orthography. Children showed robust learning for novel spelling patterns after incidental exposure to orthography. Further, we observed stronger learning for nonword-referent pairings trained with orthography. The degree of orthographic facilitation observed in posttests was related to children's reading levels, with more advanced readers showing more benefit from the presence of orthography
Self-testing through EPR-steering
The verification of quantum devices is an important aspect of quantum information, especially with the emergence of more advanced experimental implementations of quantum computation and secure communication. Within this, the theory of device-independent robust self-testing via Bell tests has reached a level of maturity now that many quantum states and measurements can be verified without direct access to the quantum systems: interaction with the devices is solely classical. However, the requirements for this robust level of verification are daunting and require high levels of experimental accuracy. In this paper we discuss the possibility of self-testing where we only have direct access to one part of the quantum device. This motivates the study of self-testing via EPR-steering, an intermediate form of entanglement verification between full state tomography and Bell tests. Quantum non-locality implies EPR-steering so results in the former can apply in the latter, but we ask what advantages may be gleaned from the latter over the former given that one can do partial state tomography? We show that in the case of self-testing a maximally entangled two-qubit state, or ebit, EPR-steering allows for simpler analysis and better error tolerance than in the case of full device-independence. On the other hand, this improvement is only a constant improvement and (up to constants) is the best one can hope for. Finally, we indicate that the main advantage in self-testing based on EPR-steering could be in the case of self-testing multi-partite quantum states and measurements. For example, it may be easier to establish a tensor product structure for a particular party’s Hilbert space even if we do not have access to their part of the global quantum system
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