Decoherence-free Subspaces Research Articles

Efficient quantum communication under collective noise

We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved, while at the same time encoding and decoding operations can be efficiently implemented. The encoding and decoding circuit requires a number of elementary gates that scale linearly with the number of transmitted qudits, $m$. The logical depth of our encoding and decoding operations is constant and depends only on the channel in question. For channels described by an arbitrary discrete group $G$, i.e.~with a discrete number, $\lvert G\rvert$, of possible noise operators, perfect transmission at a rate $m/(m+r)$ is achieved with an overhead that scales at most as $\mathcal{O}(d^r)$ where the number of auxiliary qudits, $r$, depends solely on the group in question. Moreover, this overhead is independent of the number of transmitted qudits, $m$. For certain groups, e.g.~cyclic groups, we find that the overhead scales only linearly with the number of group elements $|G|$.

Control of quantum states in decoherence-free subspaces

The problem of quantum state control in open quantum systems based on the Lyapunov method is studied. The control laws are designed to drive the system to a pure target state in decoherence-free subspace (DFS) in the interaction picture, where the average of an observable operator P is chosen as a Lyapunov function. By analyzing the positive limit set via Barbalat's lemma, we propose a sufficient condition on the observable operator such that the positive limit set only contains the target state. Under this condition, it is proved that the control laws can drive the open system to any pure target state in DFS in the interaction picture. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical simulations on a three-level system validate the effectiveness of the proposed control strategy.

Numerical method for finding decoherence-free subspaces and its applications

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum channel. We prove that this algorithm will work for all cases with probability 1, and it is more efficient than the algorithm proposed by J. A. Holbrook, D. W. Kribs, and R. Laflamme, [Quantum. Inf. Proc. 80, 381 (2003)]. In fact, our results reveal that this previous algorithm only works for special cases. As an application, we discuss how this method can be applied to increase the efficiency of an optimization procedure for finding an approximate DFS.

Quantum combinatorial model of gene expression

We propose that the DNA within the chromatin behaves as a dynamic combinatorial library capable of forming novel structures by reversible processes. We also hypothesize that states within the library may be linked via quantum tunneling. RNA polymerase then could scan these states and the system decoheres to the “appropriate” state. Two ways of sustaining quantum coherence at relevant time scales could be possible, first, screening: the quantum system can be kept isolated from its decohering environment, second, the existence of decoherence free subspaces .We discuss the role of superconductivity in context of avoiding decoherence in context of our hypothesis.

ON APPLICATIONS OF PI-ALGEBRAS IN THE ANALYSIS OF QUANTUM CHANNELS

In this paper, we discuss some constructive procedures which can be used in characterizations of linear transformations which preserve the set of states of a fixed quantum system. Our methods are based on analyzing an explicit form of a linear positive map in its Kraus representation. In particular, we discuss the so-called partial commutativity of operators and its applications to investigation of decoherence-free subspaces. These subspaces can also be considered as a special class of quantum error correcting codes. Using the concept of standard polynomials and Amitsur–Levitzki theorem and other ideas from the so-called polynomial identity algebras (PI-algebras) we discuss some effective algorithms for analyzing properties of quantum channels.

Probabilistic Multiparty Joint Remote Preparation of an Arbitrary m-Qubit State with a Pure Entangled Channel Against Collective Noise

We present a scheme for multiparty joint remote preparation of an arbitrary m-qubit state with a multiparticle entangled quantum channel against collective noise. All the senders share the information of the prepared state and perform corresponding measurement according to their knowledge of the prepared state, the receiver can reconstruct the original state by performing corresponding unitary operation on his particles if he cooperates with all the senders. Moreover, the agents use decoherence-free subspace to tolerate the collective noise. This scheme has the advantage of having high success probability for multiparty joint remote preparation of an arbitrary m-qubit state via pure entangled states.

Identification of decoherence-free subspaces without quantum process tomography

Characterizing a quantum process is the critical first step towards applying such a process in a quantum information protocol. Full process characterization is known to be extremely resource-intensive, motivating the search for more efficient ways to extract salient information about the process. An example is the identification of ``decoherence-free subspaces,'' in which computation or communications may be carried out, immune to the principal sources of decoherence in the system. Here we propose and demonstrate a protocol which enables one to directly identify a decoherence-free subspace (DFS) without carrying out a full reconstruction. Our protocol offers an up-to-quadratic speedup over standard process tomography. In this paper, we experimentally identify the DFS of a two-qubit process with 32 measurements rather than the usual 256, characterize the robustness and efficiency of the protocol, and discuss its extension to higher-dimensional systems.

State transfer based on decoherence-free target state by Lyapunov-based control

We propose a Lyapunov-based control approach for state transfer based on the decoherence-free target state. The expected target state is constructed to be a decoherence-free state in a decoherence-free subspace (DFS) by an external laser field I, so that the system state can be decoupled from the environment, and no more decoherence process will occur. With the decoherence-free target state, we design a Lyapunov-based control field II to steer the given initial state to the decoherence-free state of open quantum systems as completely as possible, and decouple the system state from the environment at the same time. In the end, it is verified that the state transfer control designed comes true on a Λ-type four-level atomic system, and the system can stay on the decoherence-free target state without coupling to environment.

Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

The evolution and stability of quantum correlations in dissipative cavity

We investigate the dynamics of quantum correlations such as entanglement and quantum discord between two atoms in a lossy cavity. It is found that a stable quantum discord could be induced even when the atoms remain separable at all times. Also, we show that it is possible to amplify and protect the quantum discord under cavity decay for certain types of initial states. Moreover, entanglement decoherence-free subspaces are obtained which may be useful in quantum information and quantum computation.

Universal quantum computation in a decoherence-free subspace for theσ̂x-type collective noise with superconducting charge qubits

Universal quantum computation in a decoherence-free subspace for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>σ</mml:mi><mml:mo>̂</mml:mo></mml:mover><mml:mi>x</mml:mi></mml:msub></mml:math>-type collective noise with superconducting charge qubits

Time-dependent decoherence-free subspace

With time-dependent Lindblad operators, an open system may have a time-dependent decoherence-free subspace (t-DFS). In this paper, we define the t-DFS and present a necessary and sufficient condition for the t-DFS. Two examples are presented to illustrate the t-DFS, which show that this t-DFS is not trivial, when the dimension of the t-DFS varies.

Dynamically stabilized decoherence-free states in non-Markovian open fermionic systems

Decoherence-free subspaces (DFSs) provide a strategy for protecting the dynamics of an open system from decoherence induced by the system-environment interaction. So far, DFSs have been primarily studied in the framework of Markovian master equations. In this work, we study decoherence-free (DF) states in the general setting of a non-Markovian fermionic environment. We identify the DF states by diagonalizing the nonunitary evolution operator for a two-level fermionic system attached to an electron reservoir. By solving the exact master equation, we show that DF states can be stabilized dynamically.

Quantum gate operations in decoherence-free fashion with separate nitrogen-vacancy centers coupled to a whispering-gallery mode resonator

We propose a scheme to achieve quantum gate operations within decoherence-free subspace (DFS) using nitrogen-vacancy centers in separate diamond nanocrystals coupled to a whispering-gallery mode resonator. By virtue of Raman transitions in the dispersive regime, we present two different methods for realizing quantum gating within DFS in a deterministic way. The quantum gating is seriously treated by considering all kinds of decoherence mechanisms, and the experimental feasibility is achieved using currently available technology.

Geometric entangling gates for coupled cavity system in decoherence-free subspaces

We propose a scheme to implement geometric entangling gates for two logical qubits in a coupled cavity system in decoherence-free subspaces. Each logical qubit is encoded with two atoms trapped in a single cavity and the geometric entangling gates are achieved by cavity coupling and controlling the external classical laser fields. Based on the coupled cavity system, the scheme allows the scalability for quantum computing and relaxes the requirement for individually addressing atoms.

Improved QSDC Protocol over a Collective-Dephasing Noise Channel

Recently, Ge and Liu (Chin. Phys. Lett. 24(10):2727–2729, 2007) proposed a quantum secure direct communication (QSDC) protocol using a decoherence-free subspace (DFS) against collective-dephasing noise. Users of their protocol can directly recover the secret message after quantum transmission without transmission of any additional classical information except for the eavesdropping check. This study points out a pitfall in Ge and Liu’s scheme, in which an eavesdropper can deliberately modify the message without being detected. Furthermore, an enhanced scheme is proposed to avoid the modification attack and to improve the qubit efficiency from 8.3 % to 12.5 %.

Capacity of multiple-input multiple-output quantum depolarizing channels

Decoherence-free subspaces (DFS) are to utilize the symmetric properties of the interaction between the system and environment so that they can be tolerant against the effect of decoherence. In this paper, we propose multiple-input multiple-output (MIMO) scheme to drive a finite-dimensional quantum system into DFS. For quantum system, the scheme is not only immune to dephasing but also feasible with currently available technology. Motivated by Shannon mutual information, we derive the capacity of MIMO quantum depolarizing channels.

Universal quantum logic gates in decoherence-free subspace with atoms trapped in distant cavities

We propose a scheme for implementation of a universal set of quantum logic gates in decoherence-free subspace with atoms trapped in distant cavities connected by optical fibers. The selective dispersive couplings between the ground states and the first-excited states of the atom-cavity-fiber system produce a state-dependent Stark shift, which can be used to implement nonlocal phase gates between two logic qubits. The single-logic-qubit quantum gates are achieved by the local two-atom collision and the Stark shift of a single atom. During all the logic operations, the logic qubits remain in decoherence-free subspace and thus the operation is immune to collective dephasing.

Death and revival of the quantum discord and the measurement-induced disturbance

Three different quantifiers, entanglement of formation (ENT), quantum discord (QD), and measurement-induced disturbance (MID), are used to measure the quantum correlations of two qubits in a common squeezed bath. A subspace was found for initial conditions in a squeezed bath, where the system experiences no decoherence. We relate the three measurements with the &#x201C;distance&#x201D; from the initial condition to the decoherence free subspace, in order to study the effect of the decoherence in the quantum correlations. We show examples of a system with quantum correlations even when entanglement is null. Furthermore, we study the necessary conditions for the system to become truly classical. We found that, under certain initial conditions and at specific times, the system becomes classical and both the QD and the MID vanish, thus observing the phenomena of sudden death and revival of the quantum correlations. Finally, we observe discontinuities in the QD.

RESEARCH ON THE RELATIONSHIP BETWEEN THE SYMMETRICAL COUPLING AND THE NON-MARKOVIAN RELAXATION CHARACTERISTICS

We make the study of the relationship between symmetrical coupling of coupling qubits and non-Markovian relaxation characteristics by utilizing concurrence. The results show that the relaxation characteristics of quantum system strongly depend on the coupling way between qubits and environment and the decoherence-free subspace may form under certain conditions. We find that when the system is initially at [Formula: see text] state or the mixed state generated by this state, we can make the quantum system always at the entangled state without entanglement sudden death (ESD) phenomenon by regulating the coupling between qubits and environment at complete anti-symmetric state. In contrast, when the system is initially at [Formula: see text] state or the mixed state generated by this state, then we must regulate the coupling way between qubits and environment at complete symmetric state to make the quantum system maintain at the entanglement state.