Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy ...Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time. Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.展开更多
We obtain a lower bound on the spacetime-weighted average of the energy density for the scalar field in four-dimensional flat spacetime. The bound takes the form of a quantum inequality. The inequality does not rely o...We obtain a lower bound on the spacetime-weighted average of the energy density for the scalar field in four-dimensional flat spacetime. The bound takes the form of a quantum inequality. The inequality does not rely on the quantum state and its form is only related to the weights, namely the spacetime sampling functions which are assumed to be smooth, positive and compactly supported. It is found that the inequality is just equal to the temporal quantum energy inequality. When the characteristic length of the temporal sampling function tends to zero, the lower bound becomes divergent. This is consistent with the fact that the spatial restriction on negative energy density does not exist in four-dimensional spacetime.展开更多
This paper investigates the quantum Dirac field in n ＋ 1-dimensional flat spacetime and derives a lower bound in the form of quantum inequality on the energy density averaged against spacetime sampling functions. The...This paper investigates the quantum Dirac field in n ＋ 1-dimensional flat spacetime and derives a lower bound in the form of quantum inequality on the energy density averaged against spacetime sampling functions. The stateindependent quantum inequality derived in the present paper is similar to the temporal quantum energy inequality and it is stronger for massive field than for massless one. It also presents the concrete results of the quantum inequality in 2 and 4-dimensional spacetimes.展开更多
The NOT gate that flips a classical bit is ubiquitous in classical information processing.However its quantum analogue,the universal NOT(UNOT) gate that flips a quantum spin in any alignment into its antipodal counter...The NOT gate that flips a classical bit is ubiquitous in classical information processing.However its quantum analogue,the universal NOT(UNOT) gate that flips a quantum spin in any alignment into its antipodal counterpart is strictly forbidden.Here we explore the connection between this discrepancy and how UNOT gates affect classical and quantum correlations.We show that while a UNOT gate always preserves classical correlations between two spins,it can non-locally increase or decrease their shared discord in ways that allow violation of the data processing inequality.We experimentally illustrate this using a multi-level trapped ^(171)Yb^+ ion that allows simulation of anti-unitary operations.展开更多
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10375023 and 10125521, the Program for New Century Excellent Talents under Grant No. 04-0784, the Key Project of the Ministry of Education under Grant No. 205110, and the 973 State Key Basic Research and Development Program of China under Grant No. G2000077400
文摘Although quantum field theory allows the local energy density negative, it also places severe restrictions on the negative energy. One of the restrictions is the quantum energy inequality （QEI）, in which the energy density is averaged over time, or space, or over space and time. By now temporal QEIs have been established for various quantum fields, but less work has been done for the spacetime quantum energy inequality. In this paper we deal with the free Rarita-Schwinger field and present a quantum inequality bound on the energy density averaged over space and time. Comparison with the QEI for the Rarita-Schwinger field shows that the lower bound is the same with the QEI. At the same time, we find the quantum inequality for the Rarita-Schwinger field is weaker than those for the scalar and Dirac fields. This fact gives further support to the conjecture that the more freedom the field has, the more easily the field displays negative energy density and the weaker the quantum inequality becomes.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10375023, 10575035 and 10125521, the Program for NCET （No 04-0784）, the Key Project of Chinese Ministry of Education （No 205110）, and the National Major State Basic Research and Development Programme of China （G2000077400）.
文摘We obtain a lower bound on the spacetime-weighted average of the energy density for the scalar field in four-dimensional flat spacetime. The bound takes the form of a quantum inequality. The inequality does not rely on the quantum state and its form is only related to the weights, namely the spacetime sampling functions which are assumed to be smooth, positive and compactly supported. It is found that the inequality is just equal to the temporal quantum energy inequality. When the characteristic length of the temporal sampling function tends to zero, the lower bound becomes divergent. This is consistent with the fact that the spatial restriction on negative energy density does not exist in four-dimensional spacetime.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10375023, 10575035 and 10125521）, the Program for New Century Excellent Talents in University （Grant No 04-0784）, the Key Project of Chinese Ministry of Education （Grant No 205110）, and the 973 National Major State Basic Research and Development of China （Grant No G2000077400）.Acknowledgments Shu W X thanks Dr Wang Zai Jun and Dr Xu Chang for helpful discussions and the staff of the Department of Mathematics for their hospitality and inspiring advice. Especially, Shu W X thanks Wu Qin for stimulating comments.
文摘This paper investigates the quantum Dirac field in n ＋ 1-dimensional flat spacetime and derives a lower bound in the form of quantum inequality on the energy density averaged against spacetime sampling functions. The stateindependent quantum inequality derived in the present paper is similar to the temporal quantum energy inequality and it is stronger for massive field than for massless one. It also presents the concrete results of the quantum inequality in 2 and 4-dimensional spacetimes.
基金supported by the National Key Research and Development Program of China(2016YFA0301901)the National Natural Science Foundation of China(11374178 and 11574002)+3 种基金the National Research Foundation of Singapore(NRF Award No.NRF-NRFF2016-02 and project NRF2017-NRFANR004 Van Qu Te)the Competitive Research Programme(CRP Award No.NRF-CRP14-2014-02)the Ministry of Education in Singapore Tier 1 RG190/17the Oxford Martin School
文摘The NOT gate that flips a classical bit is ubiquitous in classical information processing.However its quantum analogue,the universal NOT(UNOT) gate that flips a quantum spin in any alignment into its antipodal counterpart is strictly forbidden.Here we explore the connection between this discrepancy and how UNOT gates affect classical and quantum correlations.We show that while a UNOT gate always preserves classical correlations between two spins,it can non-locally increase or decrease their shared discord in ways that allow violation of the data processing inequality.We experimentally illustrate this using a multi-level trapped ^(171)Yb^+ ion that allows simulation of anti-unitary operations.
