General Quantum Operations Research Articles

Generalized duality quantum computers acting on mixed states

A generalized duality quantum computer acting on mixed states (GDQC-MS) is established, which is a device consisting of a generalized quantum wave divider, a finite number of generalized quantum operations, and a generalized quantum wave combiner. Some of the interesting properties of a GDQC are explored. For example, it is proved that the divider and the combiner of a GDQC-MS are mutually dual contractions, and when the generalized quantum operations used in a GDQC-MS are contractions, the GDQC-MS is also a contraction. In that case, the loss of an input state passing through a GDQC-MS is measured and the corresponding operator of a GDQC-MS is a generalized quantum operation.

Measurement-induced nonlocality based on the trace norm

Nonlocality is one unique property of quantum mechanics that differs from the classical world. One of its quantifications can be properly described as the maximum global effect caused by locally invariant measurements, known as measurement-induced nonlocality (MIN) (2011 Phys. Rev. Lett. 106 120401). Here, we propose quantifying the MIN by the trace norm. We show explicitly that this measure is monotonically decreasing under the action of a completely positive trace-preserving map, which is the general local quantum operation, on the unmeasured party for the bipartite state. This property avoids the undesirable characteristic appearing in the known measure of MIN defined by the Hilbert–Schmidt norm which may be increased or decreased by trivial local reversible operations on the unmeasured party. We obtain analytical formulas of the trace-norm MIN for any -dimensional pure state, two-qubit state, and certain high-dimensional states. As with other quantum correlation measures, the newly defined MIN can be directly applied to various models for physical interpretations.

On hybrid models of quantum finite automata

In the literature, there exist several interesting hybrid models of quantum finite automata (QFA) which have both quantum and classical states. This paper describes these models in a uniform way: a hybrid QFA can be seen as a two-component communication system consisting of a quantum component and a classical one, and the existing hybrid QFA differ from each other mainly in the specific communication pattern: classical-quantum, or quantum-classical, or two-way. We clarify the relationship between these hybrid QFA and some other models; in particular, it is shown that hybrid QFA can be simulated exactly by QFA with general quantum operations. As corollaries, some results in the literature concerning the language recognition power and the equivalence problem of hybrid QFA follow directly from these relationships clarified in this paper.

Ambiguous Discrimination of General Quantum Operations

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.

Observation of decoherence-induced exchange symmetry breaking in an entangled state

One of the most intriguing features of entanglement is that entangled quantum systems exhibit exchange symmetry; that is, local quantum operations on the subsystems may be interchanged without affecting the quantum state. In this work, we investigate whether the exchange symmetry is preserved for the weak (or partial collapse) measurement, a type of quantum operation, in the presence of decoherence. Demonstrated using two entangled photonic polarization qubits, the experimental results clearly show that the exchange symmetry is broken once decoherence is introduced, even though the photons still share nonzero entanglement. Our results shed light on quantum state manipulation using general quantum operations on entangled quantum states in the presence of decoherence.

General non-markovian structure of Gaussian master and stochastic Schrödinger equations.

General open quantum systems display memory features, their master equations are non-Markovian. We show that the subclass of Gaussian non-Markovian open system dynamics is tractable in a depth similar to the Markovian class. The structure of master equations exhibits a transparent generalization of the Lindblad structure. We find and parametrize the class of stochastic Schrödinger equations that unravel a given master equation, such a class was previously known for Markovian systems only. We show that particular non-Markovian unravelings known in the literature are special cases of our class.

Strong local passivity in finite quantum systems.

Passive states of quantum systems are states from which no system energy can be extracted by any cyclic (unitary) process. Gibbs states of all temperatures are passive. Strong local (SL) passive states are defined to allow any general quantum operation, but the operation is required to be local, being applied only to a specific subsystem. Any mixture of eigenstates in a system-dependent neighborhood of a nondegenerate entangled ground state is found to be SL passive. In particular, Gibbs states are SL passive with respect to a subsystem only at or below a critical system-dependent temperature. SL passivity is associated in many-body systems with the presence of ground state entanglement in a way suggestive of collective quantum phenomena such as quantum phase transitions, superconductivity, and the quantum Hall effect. The presence of SL passivity is detailed for some simple spin systems where it is found that SL passivity is neither confined to systems of only a few particles nor limited to the near vicinity of the ground state.

The range of generalized quantum operations

A completely positive map Φ is called a generalized quantum operation if tr(Φ(A))⩽tr(A) for all positive operators A. In this note, we mainly characterize the sets of {Φ(B):Φ is a generalized quantum operation}, {Φ(B):Φ† is a generalized quantum operation}, and {Φ(B):Φ and Φ† are generalized quantum operations}, where Φ† is a dual of Φ and B is a self-adjoint operator. In particular, the third set is relevant to Uhlmann's theorem in quantum information.

Quantum energy teleportation between spin particles in a Gibbs state

Energy in a multipartite quantum system appears from an operational perspective to be distributed to some extent non-locally because of correlations extant among the system's components. This non-locality allows users to transfer, in effect, locally accessible energy between sites of different system components by local operations and classical communication (LOCC). Quantum energy teleportation is a three-step LOCC protocol, accomplished without an external energy carrier, for effectively transferring energy between two physically separated, but correlated, sites. We apply this LOCC teleportation protocol to a model Heisenberg spin particle pair initially in a quantum thermal Gibbs state, making temperature an explicit parameter. We find in this setting that energy teleportation is possible at any temperature, even at temperatures above the threshold where the particles' entanglement vanishes. This shows for Gibbs spin states that entanglement is not fundamentally necessary for energy teleportation; correlation other than entanglement can suffice. Dissonance—quantum correlation in separable states—is in this regard shown to be a quantum resource for energy teleportation, more dissonance being consistently associated with greater energy yield. We compare energy teleportation from particle A to B in Gibbs states with direct local energy extraction by a general quantum operation on B and find a temperature threshold below which energy extraction by a local operation is impossible. This threshold delineates essentially two regimes: a high temperature regime where entanglement vanishes and the teleportation generated by other quantum correlations yields only vanishingly little energy relative to local extraction and a second low-temperature teleportation regime where energy is available at B only by teleportation.

Quantum Zeno effect of general quantum operations

In this paper, we show that the quantum Zeno effect occurs for any frequent quantum measurements or operations. As a result of the Zeno effect, for non-selective measurements (or trace preserving completely positive maps), the evolution of a measurement invariant state is governed by an effective Hamiltonian defined by the measurements and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, while some physical quantities (operators) still evolve as the effective dynamics.

Survival of coherence for open quantum systems in thermal baths

The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.

Experimental implementation of a fully controllable depolarizing quantum operation

The depolarizing quantum operation plays an important role in studying the quantum noise effect and implementing general quantum operations. In this work, we report a scheme which implements a fully controllable input-state independent depolarizing quantum operation for a photonic polarization qubit.

Some Properties of Generalized Quantum Operations

Let \(\mathcal{B}(\mathcal{H})\) be the set of all bounded linear operators on the separable Hilbert space \(\mathcal{H}\). A (generalized) quantum operation is a bounded linear operator defined on \(\mathcal{B}(\mathcal{H})\), which has the form \(\varPhi_{\mathcal{A}}(X)=\sum_{i=1}^{\infty}A_{i}XA_{i}^{*}\), where \(A_{i}\in\mathcal{B}(\mathcal{H})\) (i=1,2,…) satisfy \(\sum_{i=1}^{\infty}A_{i}A_{i}^{*}\leq \nobreak I\) in the strong operator topology. In this paper, we establish the relationship between the (generalized) quantum operation \(\varPhi_{\mathcal{A}}\) and its dual \(\varPhi_{\mathcal {A}}^{\dag}\) with respect to the set of fixed points and the noiseless subspace. In particular, we also partially characterize the extreme points of the set of all (generalized) quantum operations and give some equivalent conditions for the correctable quantum channel.

Quantum voting protocols based on the non-symmetric quantum channel with controlled quantum operation teleportation

In the paper, we present a kind of quantum voting protocol, which is based on controlled quantum teleportation of local unitary operations in non-symmetric quantum channel. In this protocol, the umpire CA with zero knowledge proof quantum identity authentication ensures voter’s anonymous identity authentication. The counting institution Bob generates a high-dimensional Greenberger-Horne-Zeilinger entangled state to establish a high-dimensional quantum communication channel. Performing the local unitary operation on their low-dimensional quantum ballot, voter’s quantum vote is teleportated by asymmetric matrix measurement and scrutineer Charlie auxiliary measuring. With the scrutineer Charlie’s help, Bob achieves the voting result by the output of unitary operation. Compared with other general quantum operation teleportation quantum voting protocol, the protocol utilizes the quantum information and transmission of quantum channel, which have different dimensions, so single particle information cannot be stolen, and can prevent forgery. The electoral process is fair and undeniable, owing to Charlie’s supervision. Since the success probability of quantum teleportation of local unitary operations is 1, the quantum voting is reliable.

Fast dynamics of molecular bridges

We address the dynamics of open quantum systems, in which complex finite time initial conditions, an ensuing rapid non-equilibrium transient, quantum interferences and their attenuation play important roles. To study all these phenomena in conditions of general non-equilibrium, open systems are represented by a simple structure of a molecular island between two leads. We treat this model using the non-equilibrium Green functions (NGF) method for a finite initial condition. We demonstrate that the non-interacting molecular bridge model captures well many features of general open quantum systems. Three stages of its non-equilibrium evolution, the first described by the full NGF description, the second ruled by the asymptotically exact generalized master equation and the third governed by a Markovian master equation, are delineated and related to each other.

Mocking up a Dephasing Channel with a Minimal-Sized Environment

In order to model the most general quantum operation on a d-dimensional system, a d2-dimensional environment is usually needed. We focus on the quantum dephasing process and find that this channel can be modeled by an environment with the size of at most d dimensions. An experimentally accessible matrix D is defined to characterize the dephasing channel and the minimal number of Kraus operators of the channel from the matrix I) for mocking up the dephasing channel is presented in the minimal-sized environment. An experimental simulation of dephasing channels by means of nuclear magnetic resonance techniques is carried out to justify the idea.

A Note on Fixed Points of General Quantum Operations

The fixed points of general quantum operations are considered. We characterize the set of fixed points of a general quantum operation and discuss some equivalent and sufficient conditions for this set to be nontrivial. Moreover, we also consider completely disturbed points of quantum operations.

Characterizations of fixed points of quantum operations

Let \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}$\end{document}φA be a general quantum operation. An operator B is said to be a fixed point of \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}},$\end{document}φA, if \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}(B)=B.$\end{document}φA(B)=B. In this note, we shall show conditions under which B, a fixed point \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}},$\end{document}φA, implies that B is compatible with the operation element of \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}.$\end{document}φA. In particular, we offer an extension of the generalized Lüders theorem.

A Class of General Quantum Operations

In this paper, we study the fixed points sets of a class of general quantum operations. We show that under some conditions, the fixed points sets of this class of quantum operations are trivial. Finally, we offer a sufficient and necessary condition in a special setting to ensure the fixed points sets are non-trivial.

Generalized quantum operations and almost sharp quantum effects

In this paper, we study generalized quantum operations and almost sharp quantum effects, our results generalize and improve some important conclusions in [2] and [3].