scholarly journals Quantum-enhanced secure delegated classical computing

2016 ◽  
pp. 61-86
Author(s):  
Vedran Dunjko ◽  
Theodoros Kapourniotis ◽  
Elham Kashefi
Keyword(s):  
Quantum Computing ◽  
Quantum Communication ◽  
Quantum Correlations ◽  
Computational Power ◽  
Classical Computing ◽  
Computing Capacity

We present a family of quantumly-enhanced protocols to achieve unconditionally secure delegated classical computation where the client and the server have both their classical and quantum computing capacity limited. We prove the same task cannot be achieved using only classical protocols. This extends the work of Anders and Browne on the computational power of correlations to a security setting. In doing so we are able to highlight the power of online quantum communication as we prove the same task could not be achieved using pre-shared (offline) quantum correlations.

Entanglement and other quantum correlations of a single qudit state

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560006 ◽  
Author(s):  
Margarita A. Man'ko ◽  
Vladimir I. Man'ko
Keyword(s):  
Quantum Computing ◽  
Quantum Communication ◽  
Quantum Correlations ◽  
Arbitrary Spin ◽  
Entropic Inequalities ◽  
Strong Subadditivity ◽  
Subadditivity Condition ◽  
New Information ◽  
Single Qudit ◽  
Information And Entropic Inequalities

The approach to extend the notion of entanglement for characterizing the properties of quantum correlations in the state of a single qudit is presented. New information and entropic inequalities, such as the subadditivity condition, strong subadditivity condition, and monotonicity of relative entropy for a single qudit corresponding to an arbitrary spin state with spin j are discussed. The idea to employ quantum correlations in the single-qudit state, such as the entanglement, for developing a new quantum technique in quantum computing and quantum communication is proposed. Examples of qutrit and qudit with j = 3/2 are considered.

scholarly journals Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

scholarly journals Optimal teleportation via noisy quantum channels without additional qubit resources

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Dong-Gil Im ◽  
Chung-Hyun Lee ◽  
Yosep Kim ◽  
Hyunchul Nha ◽  
M. S. Kim ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Teleportation ◽  
Quantum Communication ◽  
Quantum Noise ◽  
Single Copy ◽  
Entangled State ◽  
Quantum Network ◽  
Quantum Channels ◽  
Maximally Entangled State ◽  
Near Term

AbstractQuantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.

On the classical character of control fields in quantum information processing

2002 ◽  
Vol 2 (1) ◽  
pp. 1-13
Author(s):  
S.J. van Enk ◽  
H.J. Kimble
Keyword(s):  
Quantum Computing ◽  
Information Processing ◽  
Quantum Information ◽  
Laser Beam ◽  
Quantum State ◽  
Quantum Communication ◽  
Quantum Information Processing ◽  
Laser Fields ◽  
Undesirable Property

Control fields in quantum information processing are almost by definition assumed to be classical. In reality, however, when such a field is used to manipulate the quantum state of qubits, the qubits always become slightly entangled with the field. For quantum information processing this is an undesirable property, as it precludes perfect quantum computing and quantum communication. Here we consider the interaction of atomic qubits with laser fields and quantify atom-field entanglement in various cases of interest. We find that the entanglement decreases with the average number of photons \bar{n} in a laser beam as $E\propto\log_2 \bar{n}/\bar{n}$ for $\bar{n}\rightarrow\infty$.

scholarly journals The computational power of matchgates and the XY interaction on arbitrary graphs

2014 ◽  
Vol 14 (11&12) ◽  
pp. 901-916
Author(s):  
Daniel J. Brod ◽  
Andrew M. Childs
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Connected Graph ◽  
Nearest Neighbor ◽  
Proper Subset ◽  
Computational Power ◽  
Arbitrary Graphs

Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we characterize the power of matchgates acting on arbitrary graphs. Specifically, we show that they are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove the same dichotomy for the XY interaction, a proper subset of matchgates related to some implementations of quantum computing.

Quantum Merlin-Arthur with Clifford Arthur

2015 ◽  
Vol 15 (15&16) ◽  
pp. 1420-1430 ◽  
Author(s):  
Tomoyuki Morimae ◽  
Masahito Hayashi ◽  
Harumichi Nishimura ◽  
Keisuke Fujii
Keyword(s):  
Quantum Computing ◽  
Computational Power ◽  
Xor Gate ◽  
Single Qubit ◽  
Qubit States

We show that the class QMA does not change even if we restrict Arthur’s computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called magic states, plus any Clifford gate operations are universal for quantum computing. If Merlin is honest, he sends the witness plus magic states to Arthur. If Merlin is malicious, he might send other states to Arthur, but Arthur can verify the correctness of magic states by himself. We also generalize the result to QIP(3): we show that the class QIP(3) does not change even if the computational power of the verifier is restricted to only Clifford gate operations (plus classical XOR gate).

Quantum computing and polynomial equations over Z_2

2005 ◽  
Vol 5 (2) ◽  
pp. 102-112
Author(s):  
C.M. Dawson ◽  
H.L. Haselgrove ◽  
A.P. Hines ◽  
D. Mortimer ◽  
M.A. Nielsen ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Finite Field ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Complexity Classes ◽  
Polynomial Equations ◽  
Computational Power ◽  
Number Of Solutions

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP/P/\#P and BQP/PP.

Quantum Algorithms

2021 ◽  
pp. 82-101
Author(s):  
Renata Wong ◽  
Amandeep Singh Bhatia
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Computer Hardware ◽  
Quantum Mechanical ◽  
Computational Power ◽  
Quantum Devices ◽  
The Core

In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.

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