Speaker
Description
While current research in quantum theory focuses on the exploitation of quantum effects in communication and computation scenarios, quantum systems are also known to be advantageous for some mechanical tasks. The most known effect is that of tunneling, but there are other less well known effects. One of those is quantum backflow [1], a phenomenon in which a free quantum particle with positive momentum can be observed to propagate backwards. More recently, Tsirelson [2] studied the probability of observing a positive value when we measure the position of a harmonic oscillator with period $T$ at times $0,T/3,2T/3$. He found that a quantum harmonic oscillator can exhibit a bigger probability of success than a classical harmonic oscillator - for which such a probability is bounded by $2/3$. This effect was recently followed up to devise novel tests for quantumness and entanglement [3,4].
We consider a scenario where a (non-relativistic) particle is evolving freely in $\mathbb{R}$. Initially confined in some region $[0,L]$, we measure its position after some time $\Delta T$ has elapsed, to determine if we can find it in the region $[a,\infty)$. We show that a quantum particle can exhibit a bigger probability of success than a classical particle with the same distribution of momentum, thus finding a new mechanical quantum effect, which we name quantum projectiles. We relate the maximum possible advantage of a quantum projectile to the so-called Bracken-Melloy constant $c_{bm}$, which is the maximal possible quantum backflow. We use this relation and an integration technique from Werner [5] to compute for the first time new upper bounds for $c_{bm}$. We study several related mechanical problems and extensions of quantum projectiles. For more details, please see [6].
References
[1] A.J.Bracken, G.F.Mellow Probability backflow and a new dimensionaless quantum number J.Phys.A:Math.Gen.27 2197 (1994).
[2]B.S.Tsirelson How often is the coordinate of a harmonic oscillator positive? quant-ph/0611147 (2006)
[3]L.H.Zaw, C.C.Aw, Z.Lasmar, V.Scarani Detecting quantumness in uniform precessions Phys.Rev.A 106, 032222 (2022)
[4]P.Jayachandran, L.H.Zaw, V.Scarani Dynamic-based entanglement witnesses for harmonic oscillators quant-ph/2210.10357
[5]R.F:Werner Wigner quantusation of arrival time and oscillator phase J.Phys. A:Math.Gen. 21, 4565 (1988)
[6]D.Trillo, T.P.Le, M.Navascués, Quantum supremacy in mechanical tasks: projectiles, rockets and quantum backflow, quant-ph/2209.00725
