On Quantum No-Broadcasting

We address the issue of one-side local broadcasting for correlations in a quantum bipartite state, and conjecture that the correlations can be broadcast if and only if they are classical–quantum, or equivalently, the quantum discord, as defined by Ollivier and Zurek (Phys Rev Lett 88:017901, 2002), vanishes. We prove this conjecture when the reduced state is maximally mixed and further provide various plausible arguments supporting this conjecture. Moreover, we demonstrate that the conjecture implies the following two elegant and fundamental no-broadcasting theorems: (1) The original no-broadcasting theorem by Barnum et al. (Phys Rev Lett 76:2818, 1996), which states that a family of quantum states can be broadcast if and only if the quantum states commute. (2) The no-local-broadcasting theorem for quantum correlations by Piani et al. (Phys Rev Lett 100:090502, 2008), which states that the correlations in a single bipartite state can be locally broadcast if and only if they are classical. The results provide an informational interpretation for classical–quantum states from an operational perspective and shed new lights on the intrinsic relation between non-commutativity and quantumness.     

Bayes' rule and hidden variables

We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.     

Distinguishability and indistinguishability by local operations and classical communication

It is well known that orthogonal quantum states can be distinguished perfectly. However, if we assume that these orthogonal quantum states are shared by spatially separated parties, the distinguishability of these shared quantum states may be completely different. We show that a set of linearly independent quantum states [formula: see text] where U(m,n) are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communication. On the other hand, any l maximally entangled states from this set are locally distinguishable if l(l-1)< or =2d. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.     

Coherence evolution in two-qubit system going through amplitude damping channel

In this paper, we analyze the evolution of quantum coherence in a two-qubit system going through the amplitude damping channel. After they have gone through this channel many times, we analyze the systems with respect to the coherence of their output states. When only one subsystem goes through the channel, frozen coherence occurs if and only if this subsystem is incoherent and an auxiliary condition is satisfied for the other subsystem. When two subsystems go through this quantum channel, quantum coherence can be frozen if and only if the two subsystems are both incoherent. We also investigate the evolution of coherence for maximally incoherent-coherent states and derive an equation for the output states after one or two subsystems have gone through the amplitude damping channel.     

Majorization criterion for distillability of a bipartite quantum state

Bipartite quantum states are classified into three categories: separable states, bound entangled states, and free entangled states. It is of great importance to characterize these families of states for the development of quantum information science. In this Letter, I show that the separable states and the bound entangled states have a common spectral property. More precisely, I prove that for undis-tillable-separable and bound entangled-states, the eigenvalue vector of the global system is majorized by that of the local system. This result constitutes a new sufficient condition for distillability of bipartite quantum states. This is achieved by proving that if a bipartite quantum state satisfies the reduction criterion for distillability, then it satisfies the majorization criterion for separability.     

Enhancement of feasibility of macroscopic quantum superposition state with the quantum Rabi-Stark model

We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system, which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator. In a low-energy subspace of the Rabi-Stark model, the dressed states and then the effective Hamiltonian of the system are given. Due to the coupling of the mechanical oscillator and the atom-cavity system, if the initial state of the atom-cavity system is one of the dressed states, the mechanical oscillator will evolve into a corresponding coherent state. Thus, if the initial state of the atom-cavity system is a superposition of two dressed states, a coherent state superposition of the mechanical oscillator can be generated. The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution. We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.     

The parity operator in quantum optical metrology

Photon number states are assigned a parity of +1 if their photon number is even and a parity of ?1 if odd. The parity operator, which is minus one to the power of the photon number operator, is a Hermitian operator and thus a quantum mechanical observable although it has no classical analogue, the concept being meaningless in the context of classical light waves. In this paper we review work on the application of the parity operator to the problem of quantum metrology for the detection of small phase shifts with quantum optical interferometry using highly entangled field states such as the so-called N00N states, and states obtained by injecting twin Fock states into a beam splitter. With such states and with the performance of parity measurements on one of the output beams of the interferometer, one can breach the standard quantum limit, or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest degree of phase sensitivity allowed by quantum mechanics for linear phase shifts. Heisenberg limit sensitivities are expected to eventually play an important role in attempts to detect gravitational waves in interferometric detection systems such as LIGO and VIRGO.     

Bidirectional Quantum States Sharing

With the help of the shared entanglement and LOCC, multidirectional quantum states sharing is considered. We first put forward a protocol for implementing four-party bidirectional states sharing (BQSS) by using eight-qubit cluster state as quantum channel. In order to extend BQSS, we generalize this protocol from four sharers to multi-sharers utilizing two multi-qubit GHZ-type states as channel, and propose two multi-party BQSS schemes. On the other hand, we generalize the three schemes from two senders to multi-senders with multi GHZ-type states of multi-qubit as quantum channel, and give a multidirectional quantum states sharing protocol. In our schemes, all receivers can reconstruct the original unknown single-qubit state if and only if all sharers can cooperate. Only Pauli operations, Bell-state measurement and single-qubit measurement are used in our schemes, so these schemes are easily realized in physical experiment and their successful probabilities are all one.     

Maximum confidence measurements via probabilistic quantum cloning

Probabilistic quantum cloning(PQC) cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.     

Additivity Relations of Quantum Correlations for Three-qubit Entangled State in Atom-cavity System

Taking advantage of quantum discord and negativity respectively, four additivity relations of quantum correlations are studied in the atom-cavity system, for three identical two-level atoms resonantly interact with a single-mode high-Q cavity simultaneously. Through numerical analysis, we find that in this model of atom-cavity system, four additivity relations of negativity are always satisfied well, no matter tripartite are in the pure states or the mixed states, while the results of quantum discord are not always satisfied. What’s more, if and only if the mixed three-atom states evolve into the pure states again, four additivity inequality relations of quantum discord and negativity become equalities simultaneously.     

Controlled Remote Implementation of an Arbitrary Single-Qubit Operation with Partially Entangled Quantum Channel

We present a scheme for controlled remote implementation of an arbitrary single-qubit operation by using partially entangled states as the quantum channel. The sender can remote implement an arbitrary single-qubit operation on the remote receiver’s quantum system via partially entangled states under the controller’s control. The success probability for controlled remote implementation of quantum operation can achieve 1 if the sender and the controller perform proper projective measurements on their entangled particles. Moreover, we also discuss the scheme for remote sharing the partially unknown operations via partially entangled quantum channel. It is shown that the quantum entanglement cost and classical communication can be reduced if the implemented operation belongs to the restrict sets.     

Tripartite Splitting Arbitrary 2-Qubit Quantum Information by Using Two Asymmetric W States

In this paper we propose a tripartite scheme for splitting an arbitrary 2-qubit quantum information by using two asymmetric W states as the quantum channel. In the schemem if the two recipients collaborate together, they can deterministically recover the quantum information by performing first a 4-qubit collective unitary operation and then two single-qubit unitary operations. In addition, since the asymmetric W states are employed as the quantum channel, the scheme is robust against decoherence.     

Quantum State Discrimination with Prior Knowledge in Noisy Quantum Channels

Discrimination between two states of a qubit is investigated, which is performed under the influence of noisy quantum channels. When prior knowledge about on the quantum states is available, the detection probability of quantum measurement is compared with that of pure guessing during the irreversible time evolution. In the case of a Markovian channel, the superiority of quantum measurement to pure guessing is lost at finite time which is determined by the prior probability and the fidelity of the quantum states. For a non-Markovian channel, however, it is possible to recover the superiority of quantum measurement even if it is lost. The effect of a system-environment initial correlation on the quantum state discrimination is also investigated.     

Preservation of Quantum Coherence for Gaussian-State Dynamics in a Non-Markovian Process

Coherence is a key resource in quantum information science.Exactly understanding and controlling the variation of coherence are vital for implementation in realistic quantum systems.Using P-representation of density matrix,we obtain the analytical solution of the master equation for the classical states in the non-Markovian process and investigate the coherent dynamics of Gaussian states.It is found that quantum coherence can be preserved in such a process if the coupling strength between system and environment exceeds a threshold value.We also discuss the characteristic function of the Gaussian states in the non-Markovian process,which provides an inevitable bridge for the control and operation of quantum coherence.     

Exciton dephasing in quantum dots due to LO-phonon coupling: an exactly solvable model

It is widely believed that, due to its discrete nature, excitonic states in a quantum dot coupled to dispersionless longitudinal-optical (LO) phonons form everlasting mixed states (exciton polarons) showing no line broadening in the spectrum. This is indeed true if the model is restricted to a limited number of excitonic states in a quantum dot. We show, however, that extending the model to a large number of states results in LO phonon-induced spectral broadening and complete decoherence of the optical response.     

A possible new electron state above liquid helium

Excited states of helium atoms have been observed in the bulk liquid. We discuss the properties of such states if created at the surface. For low quantum numbers the surface is a weak perturbation compared to the atomic excitation energy. At high quantum numbers (weakly bound states) the electron wave function is forced out of the interior of the fluid and the energy spectrum is Rydberg-like.     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

Invariants for a Class of Nongeneric Three-Qubit States

We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations are presented for a class of non-generic three-qubit mixed states. It is shown that two such states in this class are locally equivalent if and only if all these invariants have equal values for them.     

Trigonometry of Quantum States

Recently the geometry of quantum states has been under considerable development. Every good geometry deserves, if possible, an accompanying trigonometry. I will here introduce such a trigonometry to accompany the geometry of quantum states.