226 research outputs found
Adaptively correcting quantum errors with entanglement
Contrary to the assumption that most quantum error-correcting codes (QECC)
make, it is expected that phase errors are much more likely than bit errors in
physical devices. By employing the entanglement-assisted stabilizer formalism,
we develop a new kind of error-correcting protocol which can flexibly trade
error correction abilities between the two types of errors, such that high
error correction performance is achieved both in symmetric and in asymmetric
situations. The characteristics of the QECCs can be optimized in an adaptive
manner during information transmission. The proposed entanglement-assisted
QECCs require only one ebit regardless of the degree of asymmetry at a given
moment and can be decoded in polynomial time.Comment: 5 pages, final submission to ISIT 2011, Saint-Petersburg, Russi
An Adaptive Entanglement Distillation Scheme Using Quantum Low Density Parity Check Codes
Quantum low density parity check (QLDPC) codes are useful primitives for
quantum information processing because they can be encoded and decoded
efficiently. Besides, the error correcting capability of a few QLDPC codes
exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical
performance analysis of an adaptive entanglement distillation scheme using
QLDPC codes. In particular, we find that the expected yield of our adaptive
distillation scheme to combat depolarization errors exceed that of Leung and
Shor whenever the error probability is less than about 0.07 or greater than
about 0.28. This finding illustrates the effectiveness of using QLDPC codes in
entanglement distillation.Comment: 12 pages, 6 figure
Codeword Stabilized Quantum Codes for Asymmetric Channels
We discuss a method to adapt the codeword stabilized (CWS) quantum code
framework to the problem of finding asymmetric quantum codes. We focus on the
corresponding Pauli error models for amplitude damping noise and phase damping
noise. In particular, we look at codes for Pauli error models that correct one
or two amplitude damping errors. Applying local Clifford operations on graph
states, we are able to exhaustively search for all possible codes up to length
. With a similar method, we also look at codes for the Pauli error model
that detect a single amplitude error and detect multiple phase damping errors.
Many new codes with good parameters are found, including nonadditive codes and
degenerate codes.Comment: 5 page
Practical entanglement distillation scheme using recurrence method and quantum low density parity check codes
Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs spite of a high yield, the hardness of decoding a random linear code makes the use of random hashing and breeding infeasible in practice this pilot study, we analyze the performance of the recurrence method, a well-known entanglement distillation scheme, with its final random hashing or breeding procedure being replaced by various efficiently decodable quantum codes. Among all the replacements investigated, the one using a certain adaptive quantum low density parity check (QLDPC) code is found to give the highest yield for Werner states over a wide range of noise level- the yield for using this QLDPC code is higher than the first runner up by more than 25% over a wide parameter range this respect, the effectiveness of using QLDPC codes in practical entanglement distillation is illustrated. © The Author(s) 2010.published_or_final_versionSpringer Open Choice, 21 Feb 201
Quantum information in the Posner model of quantum cognition
Matthew Fisher recently postulated a mechanism by which quantum phenomena
could influence cognition: Phosphorus nuclear spins may resist decoherence for
long times, especially when in Posner molecules. The spins would serve as
biological qubits. We imagine that Fisher postulates correctly. How adroitly
could biological systems process quantum information (QI)? We establish a
framework for answering. Additionally, we construct applications of biological
qubits to quantum error correction, quantum communication, and quantum
computation. First, we posit how the QI encoded by the spins transforms as
Posner molecules form. The transformation points to a natural computational
basis for qubits in Posner molecules. From the basis, we construct a quantum
code that detects arbitrary single-qubit errors. Each molecule encodes one
qutrit. Shifting from information storage to computation, we define the model
of Posner quantum computation. To illustrate the model's quantum-communication
ability, we show how it can teleport information incoherently: A state's
weights are teleported. Dephasing results from the entangling operation's
simulation of a coarse-grained Bell measurement. Whether Posner quantum
computation is universal remains an open question. However, the model's
operations can efficiently prepare a Posner state usable as a resource in
universal measurement-based quantum computation. The state results from
deforming the Affleck-Kennedy-Lieb-Tasaki (AKLT) state and is a projected
entangled-pair state (PEPS). Finally, we show that entanglement can affect
molecular-binding rates, boosting a binding probability from 33.6% to 100% in
an example. This work opens the door for the QI-theoretic analysis of
biological qubits and Posner molecules.Comment: Published versio
Concatenated Codes for Amplitude Damping
We discuss a method to construct quantum codes correcting amplitude damping
errors via code concatenation. The inner codes are chosen as asymmetric
Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes
correcting symmetric errors, many new codes with good parameters are found,
which are better than the amplitude damping codes obtained by any previously
known construction.Comment: 5 page
Exponential Lower Bound for 2-Query Locally Decodable Codes via a Quantum Argument
A locally decodable code encodes n-bit strings x in m-bit codewords C(x), in
such a way that one can recover any bit x_i from a corrupted codeword by
querying only a few bits of that word. We use a quantum argument to prove that
LDCs with 2 classical queries need exponential length: m=2^{Omega(n)}.
Previously this was known only for linear codes (Goldreich et al. 02). Our
proof shows that a 2-query LDC can be decoded with only 1 quantum query, and
then proves an exponential lower bound for such 1-query locally
quantum-decodable codes. We also show that q quantum queries allow more
succinct LDCs than the best known LDCs with q classical queries. Finally, we
give new classical lower bounds and quantum upper bounds for the setting of
private information retrieval. In particular, we exhibit a quantum 2-server PIR
scheme with O(n^{3/10}) qubits of communication, improving upon the O(n^{1/3})
bits of communication of the best known classical 2-server PIR.Comment: 16 pages Latex. 2nd version: title changed, large parts rewritten,
some results added or improve
Structured Near-Optimal Channel-Adapted Quantum Error Correction
We present a class of numerical algorithms which adapt a quantum error
correction scheme to a channel model. Given an encoding and a channel model, it
was previously shown that the quantum operation that maximizes the average
entanglement fidelity may be calculated by a semidefinite program (SDP), which
is a convex optimization. While optimal, this recovery operation is
computationally difficult for long codes. Furthermore, the optimal recovery
operation has no structure beyond the completely positive trace preserving
(CPTP) constraint. We derive methods to generate structured channel-adapted
error recovery operations. Specifically, each recovery operation begins with a
projective error syndrome measurement. The algorithms to compute the structured
recovery operations are more scalable than the SDP and yield recovery
operations with an intuitive physical form. Using Lagrange duality, we derive
performance bounds to certify near-optimality.Comment: 18 pages, 13 figures Update: typos corrected in Appendi
Machine Learning-Enhanced Advancements in Quantum Cryptography: A Comprehensive Review and Future Prospects
Quantum cryptography has emerged as a promising paradigm for secure communication, leveraging the fundamental principles of quantum mechanics to guarantee information confidentiality and integrity. In recent years, the field of quantum cryptography has witnessed remarkable advancements, and the integration of machine learning techniques has further accelerated its progress. This research paper presents a comprehensive review of the latest developments in quantum cryptography, with a specific focus on the utilization of machine learning algorithms to enhance its capabilities. The paper begins by providing an overview of the principles underlying quantum cryptography, such as quantum key distribution (QKD) and quantum secure direct communication (QSDC). Subsequently, it highlights the limitations of traditional quantum cryptographic schemes and introduces how machine learning approaches address these challenges, leading to improved performance and security. To illustrate the synergy between quantum cryptography and machine learning, several case studies are presented, showcasing successful applications of machine learning in optimizing key aspects of quantum cryptographic protocols. These applicatiocns encompass various tasks, including error correction, key rate optimization, protocol efficiency enhancement, and adaptive protocol selection. Furthermore, the paper delves into the potential risks and vulnerabilities introduced by integrating machine learning with quantum cryptography. The discussion revolves around adversarial attacks, model vulnerabilities, and potential countermeasures to bolster the robustness of machine learning-based quantum cryptographic systems. The future prospects of this combined field are also examined, highlighting potential avenues for further research and development. These include exploring novel machine learning architectures tailored for quantum cryptographic applications, investigating the interplay between quantum computing and machine learning in cryptographic protocols, and devising hybrid approaches that synergistically harness the strengths of both fields. In conclusion, this research paper emphasizes the significance of machine learning-enhanced advancements in quantum cryptography as a transformative force in securing future communication systems. The paper serves as a valuable resource for researchers, practitioners, and policymakers interested in understanding the state-of-the-art in this multidisciplinary domain and charting the course for its future advancements
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.Comment: 14 pages, no figure
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