Can Communication Power of Separable Correlations Exceed That of Entanglement Resource?

Abstract

The scenario of remote state preparation with shared correlated quantum state and one bit of forward communication [B. Dakić et al. Nature Physics 8, 666 (2012)] is considered. Optimisation of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by means of "local operations plus classical communication" actions limited to 1 bit of forward communication. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has to use decoding which is insensitive to change of coordinate system in the plane being in question (which is the natural choice if the receive does not know the latter) or (ii) is forced to use bistochastic operations which may be imposed by physically inconvenient local thermodynamical conditions. [3]. Originally the quantum advantage in realization of those task was due to quantum entanglement. However there is a more general phenomenon of quantum correlations involving the correlations beyond entanglement (see [4] and references therein). It turned out that efficiency of the protocols involving the latter may also exceed the efficiency of any classical solution of Deutsch-Jozsa problem [5], [6] or Knill-Laflamme scheme [7]. Quite recently two proposals of application of quantum correlations beyond entanglement (QCBE) have been provided. One of them have theoretically and experimentally supported the significance of their role in the analogue of quantum dense coding [8] on the level of continuous variables. The other [9] has addressed the issue of the importance of QCBE for the remote state preparation (RSP). Since RSP is one of the significant building blocks in quantum communication the question is very important. It has already been adapted to weak entanglement scenarios including bound entanglement [10] and preliminary results concerning advantage of QCBE in specific variant of RSP have been obtained [11]. The paper [9] announces the surprising possibility of the fact that in some cases the communication power of QCBE represented by separable states may exceed that of some entangled ones. The authors have also provided the direct connection of the transfer fidelity they have chosen to measure (called geometrical discord) of quantum correlations of the resource state. However this conclusion -unlike the experimental results of the paper fully transparent and impressive -seems to be not fully justified.

Separable states improve protocols with finite randomness

“…Many quantum states that are not entangled, so-called separable states, still posses non-classical features such as those characterized by quantum discord [8][9][10][11]. The role of quantum discord in communication problems was quite extensively studied and connections were established with entanglement transformations [11][12][13][14][15][16][17], coherence of protocols [18], as well as with the performance of certain problems that can be directly compared to their classical counterparts [19][20][21]. However, the latter link with the discord is established only for classical-quantum states [19] or for problems with additional constraints such as the lack of certain reference frames [20,21].…”

Measures and applications of quantum correlations

“…A refinement of this protocol has been presented in [247], where it is argued, however, that the figure of merit P 2 A (ρ AB ) can be misleading, since it can be surpassed simply by employing the trivial protocol of B randomly preparing a pure equatorial state, regardless of the communication from A and the shared quantum resource ρ AB . Instead, the suggested figure of merit should derive from the (non-quadratic) payoff-function P m, n = m · n. Generalisations of the encoding and decoding strategies of A and B are also outlined in [247]. Instead of an LPM on the shared resource ρ AB , A can perform a more general two-outcome LGM, and send the result using one bit of classical communication to B.…”

Excessive distribution of quantum entanglement

“…Achieving this in a cheap and reliable way is essential to the development of future quantum technologies. They also reinforces the role of quantum discord as a beneficial and practically relevant quantity [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]: as discord appears to bound the entanglement gain and to allow for excessive entanglement distribution, it emerges as a key player of fundamental relevance in the context of quantum communication and networking.…”