Changliang Ren

Bell’s Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality

Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell’s nonlocality. Among which, Bell’s nonlocality is the strongest type. Bell’s nonlocality for quantum states is usually detected by violation of some Bell’s inequalities, such as Clause-Horne-Shimony-Holt inequality for two qubits. Steering is a manifestation of nonlocality intermediate between entanglement and Bell’s nonlocality. This peculiar feature has led to a curious quantum phenomenon, the one-way Einstein-Podolsky-Rosen steering. The one-way steering was an important open question presented in 2007, and positively answered in 2014 by Bowles et al., who presented a simple class of one-way steerable states in a two-qubit system with at least thirteen projective measurements. The inspiring result for the first time theoretically confirms quantum nonlocality can be fundamentally asymmetric. Here, we propose another curious quantum phenomenon: Bell nonlocal states can be constructed from some steerable states. This novel finding not only offers a distinctive way to study Bell’s nonlocality without Bell’s inequality but with steering inequality, but also may avoid locality loophole in Bell’s tests and make Bell’s nonlocality easier for demonstration. Furthermore, a nine-setting steering inequality has also been presented for developing more efficient one-way steering and detecting some Bell nonlocal states.

Simultaneous suppression of time and energy uncertainties in a single-photon frequency-comb state

A single photon prepared in a time-energy state described by a frequency comb combines the extreme precision of energy defined by a single tooth of the comb with a high sensitivity to small shifts in time defined by the narrowness of a single pulse in the long sequence of pulses that describe the frequency comb state in the time domain. We show how this simultaneous suppression of time and energy uncertainties can be described by a separation of scales and compare this with the suppression of uncertainties in the two particle correlations of an entangled state. To illustrate the sensitivity of the frequency comb states to small shifts in time and frequency, we consider the Hong-Ou-Mandel dips observed in two-photon interference when both time- and frequency shifts between the input photons are varied. It is shown that the interference of two photons in equivalent frequency comb states results in a two dimensional Hong-Ou-Mandel dip that is narrow in both time and frequency, while the corresponding entangled photon pairs are only sensitive to temporal shifts. Frequency comb states thus represent a unique and different approach towards quantum operations beyond the uncertainty limit.

Direct observation of temporal coherence by weak projective measurements of photon arrival time

We show that a weak projective measurement of photon arrival time can be realized by controllable two photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the arrival time defined by the reference pulse can be obtained from the coincidence rates conditioned by a specific output measurement. If the weak measurement is followed by a measurement of frequency, the coincidence counts reveal the complete temporal coherence of the single photon wavefunction. Significantly, the weak values of the input state can also be obtained at higher measurement strengths, so that correlations between weak measurements on separate photons can be observed and evaluated without difficulty. The method can thus be used to directly observe the non-classical statistics of time-energy entangled photons.

Analysis of the time-energy entanglement of down-converted photon pairs by correlated single-photon interference

The time-energy entanglement of down-converted photon pairs is particularly difficult to characterize because direct measurements of photon arrival times are limited by the temporal resolution of photon detection. Here, we explore an alternative possibility of characterizing the temporal coherence of two-photon wavefunctions using single photon interference with weak coherent light. Specifically, this method makes use of the fact that down-conversion generates a coherent superposition of vacuum and two-photon states, so that the coincidence count rates for photon pairs after interference with weak coherent light are given by a superposition of the two-photon wavefunction from the down-conversion with the product wavefunction defined by the weak coherent references. By observing the frequency dependent interference pattern, it is possible to reconstruct the amplitudes and the phases of the two-photon wavefunction within the bandwidth of the reference pulses used in the single photon interferences. The correlated single photon interferences therefore provide a direct map of the entangled two-photon wavefunction generated in the down-conversion process.

Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with optimal states

We study the relation between the maximal violation of Svetlichnys inequality and the mixedness of quantum states and obtain the optimal state (i.e., maximally nonlocal mixed states, or MNMS, for each value of linear entropy) to beat the Clauser-Horne-Shimony-Holt and the Svetlichny games. For the two-qubit and three-qubit MNMS, we showed that these states are also the most tolerant state against white noise, and thus serve as valuable quantum resources for such games. In particular, the quantum prediction of the MNMS decreases as the linear entropy increases, and then ceases to be nonlocal when the linear entropy reaches the critical points

Optimal GHZ Paradox for Three Qubits

{2}/{3}

Deriving Einstein–Podolsky–Rosen steering inequalities from the few-body Abner Shimony inequalities

and

How to make optimal use of maximal multipartite entanglement in clock synchronization

{9}/{14}

Whether Quantum Computation Can be Almighty

for the two- and three-qubit cases, respectively. The MNMS are related to classical errors in experimental preparation of maximally entangled states.

Precisely measuring the orbital angular momentum of beams via weak measurement

Quatum nonlocality as a valuable resource is of vital importance in quantum information processing. The characterization of the resource has been extensively investigated mainly for pure states, while relatively less is know for mixed states. Here we prove the existence of the optimal GHZ paradox by using a novel and simple method to extract an optimal state that can saturate the tradeoff relation between quantum nonlocality and the state purity. In this paradox, the logical inequality which is formulated by the GHZ-typed event probabilities can be violated maximally by the optimal state for any fixed amount of purity (or mixedness). Moreover, the optimal state can be described as a standard GHZ state suffering flipped color noise. The maximal amount of noise that the optimal state can resist is 50%. We suggest our result to be a step toward deeper understanding of the role played by the AVN proof of quantum nonlocality as a useful physical resource.