Classical Bits Research Articles

Error correction schemes for fully correlated quantum channels protecting both quantum and classical information

We study efficient quantum error correction schemes for the fully correlated channel on an n-qubit system with error operators that assume the form \(\sigma _x^{\otimes n}\), \(\sigma _y^{\otimes n}\), \(\sigma _z^{\otimes n}\). Previous schemes are improved to facilitate implementation. In particular, when n is odd and equals \(2k+1\), we describe a quantum error correction scheme using one arbitrary qubit \(\sigma \) to protect the data state \(\rho \) in a 2k-qubit system. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) only requires 3k CNOT gates (each with one control bit and one target bit). After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \({\tilde{\sigma }} \otimes \rho \) so that a partial trace operation can recover \(\rho \). When n is even and equals \(2k+2\), we describe a hybrid quantum error correction scheme using any one of the two classical bits \(\sigma \in \{|ij{\rangle }{\langle }ij|: i, j \in \{0,1\}\}\) to protect a 2k-qubit state \(\rho \) and two classical bits. The encoding operation \(\sigma \otimes \rho \mapsto \Phi (\sigma \otimes \rho )\) can be done by \(3k+2\) CNOT gates and a single-qubit Hadamard gate. After the encoded state \(\Phi (\sigma \otimes \rho )\) goes through the channel, we can apply the inverse operation \(\Phi ^{-1}\) to produce \(\sigma \otimes \rho \) so that a perfect protection of the two classical bits \(\sigma \) and the 2k-qubit state is achieved. If one uses an arbitrary two-qubit state \(\sigma \), the same scheme will protect 2k-qubit states. The scheme was implemented using MATLAB, Mathematica, Python and the IBM’s quantum computing framework qiskit.

Simple communication complexity separation from quantum state antidistinguishability

A set of $n$ pure quantum states is called antidististinguishable if there exists an $n$-outcome measurement that never outputs the outcome `$k$' on the $k$-th quantum state. We describe sets of quantum states for which any subset of three states is antidistinguishable and use this to produce a two-player communication task that can be solved with $\log d$ qubits, but requires one-way communication of at least $\log (4/3) (d-1) - 1 \approx 0.415 (d-1) - 1$ classical bits. The advantages of the approach are that the proof is simple and self-contained -- not needing, for example, to rely on hard-to-establish prior results in combinatorics -- and that with slight modifications, non-trivial bounds can be established in any dimension $\geq 3$. The task can be framed in terms of the separated parties solving a relation, and the separation is also robust to multiplicative error in the output probabilities. We show, however, that for this particular task, the separation disappears if two-way classical communication is allowed. Finally, we state a conjecture regarding antidistinguishability of sets of states, and provide some supporting numerical evidence. If the conjecture holds, then there is a two-player communication task that can be solved with $\log d$ qubits, but requires one-way communication of $\Omega (d \log d)$ classical bits.

Scheme for realizing quantum dense coding via entanglement swapping

Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to realize quantum dense coding via entanglement swapping in a cavity array containing a certain number of two-level atoms. Proper choice of system parameters such as atom–cavity and inter-cavity couplings allows perfect transfer of information. A high fidelity transfer of information is shown to be possible by using recently achieved experimental values in the context of photonic crystal cavities and superconducting resonators. To mimic experimental imperfections, disorder in both the coupling strengths and resonance frequencies is considered.

Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit

We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them, replacing classical bits by zero-bits makes teleportation asymptotically reversible. The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $\alpha$, we call the associated resource an $\alpha$-bit. Changing $\alpha$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $\alpha$-bits, including the applications above, and determine the $\alpha$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants.

Speech Encryption Algorithm Based on Nonorthogonal Quantum State with Hyperchaotic Keystreams

With the advancement in modern computational technologies like cloud computing, there has been tremendous growth in the field of data processing and encryption technologies. In this contest there is an increasing demand for successful storage of the data in the encrypted domain to avoid the possibility of data breach in shared networks. In this paper, a novel approach for speech encryption algorithm based on quantum chaotic system is designed. In the proposed method, classical bits of the speech samples are initially encoded in nonorthogonal quantum state by the secret polarizing angle. In the quantum domain, encoded speech samples are subjected to bit-flip operation according to the Controlled–NOT gate followed by Hadamard transform. Complete superposition of the quantum state in both Hadamard and standard basis is achieved through Hadamard transform. Control bits for C-NOT gate as well as Hadamard gate are generated with a modified Lu˙-hyperchaotic system. Secret nonorthogonal rotation angles and initial conditions of the hyperchaotic system are the keys used to ensure the security of the proposed algorithm. The computational complexity of the proposed algorithm has been analysed both in quantum domain and classical domain. Numerical simulation carried out based on the above principle showed that the proposed speech encryption algorithm has wider keyspace, higher key sensitivity and robust against various differential and statistical cryptographic attacks.

Fault-Tolerant Resource Estimation of Quantum Random-Access Memories

Quantum random-access look-up of a string of classical bits is a necessary ingredient in several important quantum algorithms. In some cases, the cost of such quantum random-access memory (qRAM) is the limiting factor in the implementation of the algorithm. In this paper we study the cost of fault-tolerantly implementing a qRAM. We construct and analyze generic families of circuits that function as a qRAM, discuss opportunities for qubit-time tradeoffs, and estimate their resource costs when embedded in a surface code.

Physical Layer Security Protocol for Poisson Channels for Passive Man-in-the-Middle Attack

In this work, we focus on the classical optical channel having Poissonian statistical behavior and propose a novel secrecy coding-based physical layer protocol. Our protocol is different but complementary to both (computationally secure) quantum immune cryptographic protocols and (information theoretically secure) quantum cryptographic protocols. Specifically, our (information theoretical) secrecy coding protocol secures classical digital information bits at photonic level exploiting the random nature of the Poisson channel. It is known that secrecy coding techniques for the Poisson channel based on the classical one-way wiretap channel (introduced by Wyner in 1975) ensure secret communication only if the mutual information to the eavesdropper is smaller than that to the legitimate receiver. In order to overcome such a strong limitation, we introduce a two-way protocol that always ensures secret communication independently of the conditions of legitimate and eavesdropper channels. We prove this claim showing rigorous comparative derivation and analysis of the information theoretical secrecy capacity of the classical one-way and of the proposed two-way protocols. We also show numerical calculations that prove drastic gains and strong practical potential of our proposed two-way protocol to secure information transmission over optical channels.

Quantum bit commitment on IBM QX

Quantum bit commitment (QBC) is a quantum version of the classical bit commitment security primitive. As other quantum security primitives and protocols, QBC improves on cheating detection over its classical counterpart. The implementation of the QBC protocol below relies on the use of common quantum gates: the Hadamard gate used for orthonormal bases and the CNOT gate used to swap qubits. The protocol was run and tested on IBM quantum experience (IBM QX). IBM QX offers two different quantum environments: as a simulator and as a real quantum machine. In our implementation, honest and dishonest participants were considered. Results of both the simulation and the quantum execution were compared against the theoretical expectations. The IBM QX simulator gives results that match the theoretical model. The IBM QX real computer deviates from the expected behavior by a measurable amount. Using the standard deviation and the Hamming distance, the conclusion is that the quantum computer is usable as the difference to the simulator is within an acceptable margin of error. The QBC protocol of choice is fully secure against cheating by Bob. The only way Alice can cheat is using multi-dimensional entanglement. The cost for Alice to cheat is exponential in the number of qubits used, namely $$ O(2^{6n + 3k + 1} ) $$.

Qubit exchange interactions from permutations of classical bits

In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’t[Formula: see text]Hooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

Comparison of n-LSB embedding approach in different color spaces

Today, secure communication is one of the biggest goals that people want to achieve. There are many different methods to ensure security in data communication. Steganography is one of the methods that can be used in secure data communication. In this study, n-LSB embedding method based on reducing the amount of distortion generated by the classical Least Significant Bit substitution method that we introduced in another study has been applied in both RGB color space and HSI, XYZ and YCbCr color spaces. In the embedding process, 3 message bits were embedded in each color channel. 7.94 kb data is embedded on 3 different cover images. The obtained results were compared with the PSNR criterion, which is the criterion of image quality evaluation, and it is seen that proposed n-LSB approach gives better results in HSI color space for 3 cover images. The highest PSNR value obtained was 83.907 dB.

Inner privacy of conscious experiences and quantum information

The human mind is constituted by inner, subjective, private, first-person conscious experiences that cannot be measured with physical devices or observed from an external, objective, public, third-person perspective. The qualitative, phenomenal nature of conscious experiences also cannot be communicated to others in the form of a message composed of classical bits of information. Because in a classical world everything physical is observable and communicable, it is a daunting task to explain how an empirically unobservable, incommunicable consciousness could have any physical substrates such as neurons composed of biochemical molecules, water, and electrolytes. The challenges encountered by classical physics are exemplified by a number of thought experiments including the inverted qualia argument, the private language argument, the beetle in the box argument and the knowledge argument. These thought experiments, however, do not imply that our consciousness is nonphysical and our introspective conscious testimonies are untrustworthy. The principles of classical physics have been superseded by modern quantum physics, which contains two fundamentally different kinds of physical objects: unobservable quantum state vectors, which define what physically exists, and quantum operators (observables), which define what can physically be observed. Identifying consciousness with the unobservable quantum information contained by quantum physical brain states allows for application of quantum information theorems to resolve possible paradoxes created by the inner privacy of conscious experiences, and explains how the observable brain is constructed by accessible bits of classical information that are bound by Holevo's theorem and extracted from the physically existing quantum brain upon measurement with physical devices.

Quantum computing with classical bits

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.

Quantum signature scheme based on Hadamard and Hπ/4 operators.

Based on the Hadamard and Hπ/4 operators, a new quantum signature scheme is proposed. In our scheme, the signer's private key is generated by a trusted private key generator (PKG), while the identity information of the signer is used as the corresponding public key. Both of the private key and public key of the signer are classical bit strings, which can be easily stored and reused. Given a quantum signature, anyone can verify the validity of the quantum signature with the signer's identity. Therefore, our scheme is a public-key quantum signature without a digital certificate, which has the merits of an identity-based cryptosystem and can simplify the key management of the quantum signature system. On the other hand, our scheme need not use any quantum swap test during the signature verification phase. Furthermore, by the signature proof, our scheme can arbitrate the potential disputation of losing quantum signature, which cannot be arbitrated in most of the quantum signature schemes. So our scheme has the property of strong non-repudiation. It also has the security properties of information-theoretic security, unforgeability, etc. Our scheme can achieve a high efficiency of 70%. Therefore, our quantum signature scheme is more secure, practicable, and efficient than the similar schemes.

A Novel Application of Probabilistic Teleportation: p-Rabin Quantum Oblivious Transfer of a Qubit

So far, all existing quantum oblivious transfer protocols focused on realization of the oblivious transfer of a classical bit or classical bit-string. In this paper, p-Rabin quantum oblivious transfer of a qubit protocol is achieved by using a probabilistic teleportation protocol. As the probabilistic teleportation protocol is able to transfer an (un)known pure state with a certain probability, this feature makes the probabilistic teleportation protocol well fit for Rabin oblivious transfer. Here, this is the first time that the concept of qubit oblivious transfer is presented. Furthermore, p-Rabin quantum oblivious transfer of a qubit protocol can also be used for oblivious of a bit by encoding classical bit with two pre-agreed orthogonal states. Finally, security analysis shows that the protocol satisfies the security requirements of oblivious transfer, and what’s more, the discussion of relationship with no-go theorem demonstrates that the probabilistic teleportation protocol is able to evade the no-go theorem.

Hardware-Efficient Qubit Control with Single-Flux-Quantum Pulse Sequences

The hardware overhead associated with microwave control is a major obstacle to scale-up of superconducting quantum computing. An alternative approach involves irradiation of the qubits with trains of Single Flux Quantum (SFQ) pulses, pulses of voltage whose time integral is precisely equal to the superconducting flux quantum. Here we describe the derivation and validation of compact SFQ pulse sequences in which classical bits are clocked to the qubit at a frequency that is roughly a factor 5 higher than the qubit oscillation frequency, allowing for variable pulse-to-pulse timing. The control sequences are constructed by repeated streaming of short subsequence registers that are designed to suppress leakage out of the computational manifold. With a single global clock, high-fidelity (> 99.99%) control of qubits resonating at over 20 distinct frequencies is possible. SFQ pulses can be stored locally and delivered to the qubits via a proximal classical Josephson digital circuit, offering the possibility of a streamlined, low-footprint classical coprocessor for monitoring errors and feeding back to the qubit array.

New Public-key Quantum Signature Scheme with Quantum One-Way Function

Based on the asymmetric quantum cryptosystem, a new public-key quantum signature scheme is proposed. In our scheme, the signer’s public key is derived from her public identity information, and the corresponding private key is generated by the trusted private key generator (PKG). Both of the public key and the private key are classical bit strings, so they are easily kept. It is very convenient for the key management of the quantum signature system. The signer signs a message with her private key, and the quantum signature can be publicly verified with the signer’s public key and the quantum one-way function. Both of the private key and public key can be reused. On the other hand, in the signing phase, the signer sends the message to PKG via a classical unencrypted channel, which can be used to authenticate the identity of the signer. The proposed scheme has the properties of completeness, information-theoretic security, non-repudiation and unforgeability. Its information-theoretic security is ensured by quantum indistinguishability mechanics. On the other hand, our scheme is more efficient than the similar schemes.

Local-hidden-state models for T-states using finite shared randomness

The study of local models using finite shared randomness originates from the consideration about the cost of classically simulating entanglement in composite quantum systems. We construct explicitly two families of local-hidden-state (LHS) models for T-states, by mapping the problem to the Werner state. The continuous decreasing of shared randomness along with entanglement, as the anisotropy increases, can be observed in the one from the most economical model for the Werner state. The construction of the one for separable states shows that the separable boundary of T-states can be generated from the one of the Werner state, and the cost is 2 classical bits.

Optimal quantum channel for perfect controlled super-dense coding protocol

Perfect super-dense coding protocol allows transmission of two classical bits (cbits) by sending just one quantum bit (qubit) with unit success probability. Perfect controlled super-dense coding protocol should be such that perfect super-dense coding is achieved with the controller’s cooperation. There are different possible types of quantum channels to be shared among the authorized parties to perform perfect controlled super-dense coding. Of our interest is the quantum channel which is optimal in the sense that no cbits can be transmitted with certainty without the controller’s cooperation. We attack this problem by means of the so-called control power. By calculating and analyzing the control power for specific quantum channels we figure out the one that is optimal. We also address the issue of how to prepare such optimal quantum channel.

Coulomb blockade correlations in a coupled single-electron device system

Single-electron devices, such as metal single-electron transistor (SET) and semiconductor quantum dot (QD), are Coulomb blockade (CB) devices with promising applications in both quantum and classical beyond-Si information technologies. As an example, a coupled SET-QD system can provide an experimental platform for addressing, manipulating, and detecting spin and/or charge-based qubits for quantum information processing. We have designed and fabricated a prototype device in this family: a series-coupled double quantum dot (DQD) with side-coupled and/or top-coupled Al single-electron transistors (Al-SET), and implemented the readout of the single electron charging and CB behaviors in a QD using the Al-SET. The readout operation is manifested by the correlated CB oscillations taking place separately in the SET and in the QD; these oscillations originate from that the change of electrons one by one in the QD. We have developed an electrostatics model to study the CB correlations in the capacitively coupled QD/Al-SET device system, which shows qualitative agreement with our experimental observations. Moreover, our design and device fabrication are compatible with modern semiconductor techniques, and can potentially be scaled up into larger integrated systems with quantum and classic bit operation and measurement circuitry.

One Step Quantum Key Distribution Protocol Based on the Hyperentangled Bell State

Considering the security and efficiency of quantum communication system, one step quantum key distribution protocol based on hyperentangled Bell state is proposed. Every 6 classical bits are divided into a group, which are encoded by single particle and hyperentangled Bell state, the sender Alice sends them to receiver Bob, Bob randomly selects the position of hyperentangled Bell state to measure and detects the existence of eavesdropper Eve by comparing measurement results in his hand and transmitted by Alice. Quantum key distribution protocol based on grouping is proposed to solve the storage problem of quantum information and improve the maneuverability, a security analysis is calculated under the intercept-measure-resend attack which introduce at least an error rate of 46.875%, if Eve wants to get all the information, the probability of detection eavesdropping under the entanglement-measure attack is 93.75%, so it proves that proposed protocol does not need to store the quantum state and asymptotically secure under intercept-measure-resend attack and entanglement-measure attack.