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Ranjith Nair

Publications and source records attributed to Ranjith Nair.

33 records · Page 2Linked to original sources
arXiv2015

Quantum optimality of photon counting for temperature measurement of thermal astronomical sources

Using the quantum Cramér-Rao bound from quantum estimation theory, we derive a fundamental quantum limit on the sensitivity of a temperature measurement of a thermal astronomical source. This limit is expressed in terms of the source temperature $T_s$, input spectral bandwidth $Δν$, and measurement duration $T$, subject to a long measurement time assumption $TΔν\gg 1$. It is valid for any measurement procedure that yields an unbiased estimate of the source temperature. The limit agrees with the sensitivity of direct detection or photon counting, and also with that of the ideal radiometer in the regime $kT_s/h ν_0\gg 1$ for which the Rayleigh-Jeans approximation is valid, where $ν_0$ is the center frequency at which the radiometer operates. While valid across the electromagnetic spectrum, the limit is especially relevant for radio astronomy in this regime, since it implies that no ingenious design or technological improvement can beat an ideal radiometer for temperature measurement. In this connection, our result refutes the recent claim of a radio astronomy technique with much-improved sensitivity over the radiometer (Lieu et al. 2015).

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arXiv2013

Realizable receivers for discriminating arbitrary coherent-state waveforms and multi-copy quantum states near the quantum limit

Coherent states of light, and methods for distinguishing between them, are central to all applications of laser light. We obtain the ultimate quantum limit on the error probability exponent for discriminating among any M multimode coherent-state waveforms via the quantum Chernoff exponent in M-ary multi-copy state discrimination. A receiver, i.e., a concrete realization of a quantum measurement, called the Sequential Waveform Nulling (SWN) receiver, is proposed for discriminating an arbitrary coherent-state ensemble using only auxiliary coherent-state fields, beam splitters, and non-number-resolving single photon detectors. An explicit error probability analysis of the SWN receiver is used to show that it achieves the quantum limit on the error probability exponent, which is shown to be a factor of four greater than the error probability exponent of an ideal heterodyne-detection receiver on the same ensemble. We generalize the philosophy of the SWN receiver, which is itself adapted from some existing coherent-state receivers, and propose a receiver -- the Sequential Testing (ST) receiver-- for discriminating n copies of M pure quantum states from an arbitrary Hilbert space. The ST receiver is shown to achieve the quantum Chernoff exponent in the limit of a large number of copies, and is remarkable in requiring only local operations and classical communication (LOCC) to do so. In particular, it performs adaptive copy-by-copy binary projective measurements. Apart from being of fundamental interest, these results are relevant to communication, sensing, and imaging systems that use laser light and to photonic implementations of quantum information processing protocols in general.

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arXiv2012

Fundamental quantum limits to waveform detection

Ever since the inception of gravitational-wave detectors, limits imposed by quantum mechanics to the detection of time-varying signals have been a subject of intense research and debate. Drawing insights from quantum information theory, quantum detection theory, and quantum measurement theory, here we prove lower error bounds for waveform detection via a quantum system, settling the long-standing problem. In the case of optomechanical force detection, we derive analytic expressions for the bounds in some cases of interest and discuss how the limits can be approached using quantum control techniques.

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arXiv2012

Symmetric M-ary phase discrimination using quantum-optical probe states

We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes, and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of (M - 1)/2. For the M = 2 case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate.

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arXiv2011

Optimal Quantum States for Image Sensing in Loss

We consider a general image sensing framework that includes many quantum sensing problems by an appropriate choice of image set, prior probabilities, and cost function. For any such problem, in the presence of loss and a signal energy constraint, we show that a pure input state of light with the signal modes in a mixture of number states minimizes the cost among all ancilla-assisted parallel strategies. Lossy binary phase discrimination with a peak photon number constraint and general lossless image sensing are considered as examples.

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arXiv2011

Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection

We consider the problem of distinguishing, with minimum probability of error, two optical beam-splitter channels with unequal complex-valued reflectivities using general quantum probe states entangled over M signal and M' idler mode pairs of which the signal modes are bounced off the beam splitter while the idler modes are retained losslessly. We obtain a lower bound on the output state fidelity valid for any pure input state. We define number-diagonal signal (NDS) states to be input states whose density operator in the signal modes is diagonal in the multimode number basis. For such input states, we derive series formulas for the optimal error probability, the output state fidelity, and the Chernoff-type upper bounds on the error probability. For the special cases of quantum reading of a classical digital memory and target detection (for which the reflectivities are real valued), we show that for a given input signal photon probability distribution, the fidelity is minimized by the NDS states with that distribution and that for a given average total signal energy N_s, the fidelity is minimized by any multimode Fock state with N_s total signal photons. For reading of an ideal memory, it is shown that Fock state inputs minimize the Chernoff bound. For target detection under high-loss conditions, a no-go result showing the lack of appreciable quantum advantage over coherent state transmitters is derived. A comparison of the error probability performance for quantum reading of number state and two-mode squeezed vacuum state (or EPR state) transmitters relative to coherent state transmitters is presented for various values of the reflectances. While the nonclassical states in general perform better than the coherent state, the quantitative performance gains differ depending on the values of the reflectances.

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arXiv2009

Classicalization of Nonclassical Quantum States in Loss and Noise -- Some No-Go Theorems

The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical No-Go theorem is enunciated that rules out the possibility of significant advantage of nonclassical over classical states. The recent work on quantum illumination is discussed as an example of our no-go approach.

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arXiv2008

Comment on "Exposed-Key Weakness of Alpha-Eta" [Phys. Lett. A 370 (2007) 131]

We show that the insecurity claim of the AlphaEta cryptosystem made by C. Ahn and K. Birnbaum in Phys. Lett. A 370 (2007) 131-135 under heterodyne attack is based on invalid extrapolations of Shannon's random cipher analysis and on an invalid statistical independence assumption. We show, both for standard ciphers and AlphaEta, that expressions of the kind given by Ahn and Birnbaum can at best be interpreted as security lower bounds.

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arXiv2007

On the Security of the Y-00 (AlphaEta) Direct Encryption Protocol

We review the current status of the AlphaEta direct encryption protocol. After describing AlphaEta, we summarize the main security claims made on it. We then describe recent attacks developed against it in the literature, and suggest security enhancements and future research directions based on our results.

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arXiv2006

On the Security of Y-00 under Fast Correlation and Other Attacks on the Key

The potential weakness of the Y-00 direct encryption protocol when the encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In this paper, we show how this weakness can be eliminated with a proper design of ENC. In particular, we present a Y-00 configuration that is more secure than AES under known-plaintext attack. It is also shown that under any ciphertext-only attack, full information-theoretic security on the Y-00 seed key is obtained for any ENC when proper deliberate signal randomization is employed.

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arXiv2006

Quantum Noise Randomized Ciphers

We review the notion of a classical random cipher and its advantages. We sharpen the usual description of random ciphers to a particular mathematical characterization suggested by the salient feature responsible for their increased security. We describe a concrete system known as AlphaEta and show that it is equivalent to a random cipher in which the required randomization is effected by coherent-state quantum noise. We describe the currently known security features of AlphaEta and similar systems, including lower bounds on the unicity distances against ciphertext-only and known-plaintext attacks. We show how AlphaEta used in conjunction with any standard stream cipher such as AES (Advanced Encryption Standard) provides an additional, qualitatively different layer of security from physical encryption against known-plaintext attacks on the key. We refute some claims in the literature that AlphaEta is equivalent to a non-random stream cipher.

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arXiv2006

On the security of AlphaEta: Response to `Some attacks on quantum-based cryptographic protocols'

Lo and Ko in [1] have developed some attacks on the cryptosystem called AlphaEta [2], claiming that these attacks undermine the security of AlphaEta for both direct encryption and key generation. In this paper, we show that their arguments fail in many different ways. In particular, the first attack in [1] requires channel loss or length of known-plaintext that is exponential in the key length and is unrealistic even for moderate key lengths. The second attack is a Grover search attack based on `asymptotic orthogonality' and was not analyzed quantitatively in [1]. We explain why it is not logically possible to ``pull back'' an argument valid only at n=infinity into a limit statement, let alone one valid for a finite number of transmissions n. We illustrate this by a `proof' using a similar asymptotic orthogonality argument that coherent-state BB84 is insecure for any value of loss. Even if a limit statement is true, this attack is a priori irrelevant as it requires an indefinitely large amount of known-plaintext, resources and processing. We also explain why the attacks in [1] on AlphaEta as a key-generation system are based on misinterpretations of [2]. Some misunderstandings in [1] regarding certain issues in cryptography and optical communications are also pointed out. Short of providing a security proof for AlphaEta, we provide a description of relevant results in standard cryptography and in the design of AlphaEta to put the above issues in the proper framework and to elucidate some security features of this new approach to quantum cryptography.

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arXiv2005

Reply to: 'Reply to: "Comment on: `How much security does Y-00 protocol provide us?` " '

Nishioka et al claim in [1], elaborating on their earlier paper [2], that the direct encryption scheme called Y-00 [3,4] is equivalent to a classical non-random additive stream cipher, and thus offers no more security than the latter. In this paper, we show that this claim is false and that Y-00 may be considered equivalent to a \emph{random} cipher. We explain why a random cipher provides additional security compared to its nonrandom counterpart. Some criticisms in [1] on the use of Y-00 for key generation are also briefly responded to.

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arXiv2004

Security of Y-00 and similar quantum cryptographic protocols

It is claimed in Phys. Lett. A by T. Nishioka et. al. 327 (2004) 28-32, that the security of Y-00 is equivalent to that of a classical stream cipher. In this paper it is shown that the claim is false in either the use of Y-00 for direct encryption or key generation, in all the parameter ranges it is supposed to operate including those of the experiments reported thus far. The security of Y-00 type protocols is clarified.

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